For the radioactive isotope and associated half-live (assume that d...

Question
For the radioactive isotope and associated half-live (assume that decays according to the formula A(t) = A0ekt where A0 is the initial amount of the material and k is the decay constant):
Find the decay constant k. Round your answer to four decimal places.
Find a function which gives the amount of isotope A which remains after time t. (Keep the units of A and t the same as the given data.)
Determine how long it takes for 90% of the material to decay. Round your answer to two decimal places. (HINT: If 90% of the material decays, how much is left?)

Cobalt 60, used in food irradiation, initial amount 50 grams, half-life of 5.27 years.
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      • creating: components.open-graph (199μs)
      • composing: components.open-graph (77μs)
      • creating: site.headers.header (311μs)
      • composing: site.headers.header (78μs)
      • Illuminate\Cache\Events\CacheHit (1.8ms)
      • creating: components.footer (86μs)
      • composing: components.footer (97μs)
      • Illuminate\Cache\Events\CacheHit (962μs)
      • Illuminate\Cache\Events\CacheMissed (373μs)
      • Illuminate\Database\Events\StatementPrepared (851μs)
      • Illuminate\Database\Events\QueryExecuted (1.08ms)
      • eloquent.retrieved: App\Models\SubjectCat (55μs)
      • Illuminate\Cache\Events\KeyWritten (325μs)
      • Illuminate\Cache\Events\CacheHit (331μs)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (394μs)
      • Illuminate\Cache\Events\CacheHit (345μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • creating: components.forms.contact-us (258μs)
      • composing: components.forms.contact-us (168μs)
      • creating: components.forms.get-started (186μs)
      • composing: components.forms.get-started (86μs)
      • creating: components.forms.free-tool-download (145μs)
      • composing: components.forms.free-tool-download (77μs)
      • creating: components.forms.claim-free-worksheet (142μs)
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      • creating: components.forms.tutor-subscription-waitlist (142μs)
      • composing: components.forms.tutor-subscription-waitlist (75μs)
      • creating: components.forms.tutor-subscription-join (139μs)
      • composing: components.forms.tutor-subscription-join (73μs)
      • creating: components.forms.tutor-support (146μs)
      • composing: components.forms.tutor-support (71μs)
      • 312 x Illuminate\Cache\Events\CacheHit (19.12%)
        83.77ms
        18 x Illuminate\Database\Events\StatementPrepared (4.67%)
        20.45ms
        18 x Illuminate\Database\Events\QueryExecuted (3.84%)
        16.81ms
        10 x Illuminate\Cache\Events\CacheMissed (1.81%)
        7.92ms
        10 x Illuminate\Cache\Events\KeyWritten (1.45%)
        6.35ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.35%)
        1.55ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.2%)
        862μs
        1 x Illuminate\Database\Events\ConnectionEstablished (0.15%)
        676μs
        1 x Illuminate\Routing\Events\Routing (0.14%)
        601μs
        1 x creating: site.layouts.app (0.12%)
        513μs
        1 x creating: components.canonical (0.11%)
        501μs
        1 x creating: homework.show (0.08%)
        364μs
        1 x creating: components.breadcrumbs (0.08%)
        332μs
        1 x creating: site.headers.header (0.07%)
        311μs
        1 x eloquent.booting: App\Models\SubjectCat (0.06%)
        278μs
        1 x creating: components.forms.contact-us (0.06%)
        258μs
        1 x Illuminate\Routing\Events\RouteMatched (0.05%)
        235μs
        1 x creating: components.open-graph (0.05%)
        199μs
        1 x creating: components.forms.get-started (0.04%)
        186μs
        6 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        181μs
        1 x composing: components.forms.contact-us (0.04%)
        168μs
        1 x composing: components.breadcrumbs (0.04%)
        160μs
        1 x composing: homework.show (0.04%)
        154μs
        1 x creating: components.forms.tutor-support (0.03%)
        146μs
        1 x creating: components.forms.free-tool-download (0.03%)
        145μs
        1 x creating: components.forms.claim-free-worksheet (0.03%)
        142μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.03%)
        142μs
        1 x creating: components.forms.tutor-subscription-join (0.03%)
        139μs
        1 x eloquent.booting: App\Models\Subject (0.03%)
        131μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        130μs
        1 x eloquent.retrieved: App\Models\Subject (0.03%)
        123μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        112μs
        1 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        105μs
        1 x composing: components.canonical (0.02%)
        103μs
        1 x composing: components.footer (0.02%)
        97μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        94μs
        1 x creating: components.footer (0.02%)
        86μs
        1 x composing: components.forms.get-started (0.02%)
        86μs
        1 x composing: site.headers.header (0.02%)
        78μs
        1 x composing: components.forms.free-tool-download (0.02%)
        77μs
        1 x composing: components.open-graph (0.02%)
        77μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.02%)
        75μs
        1 x composing: components.forms.claim-free-worksheet (0.02%)
        74μs
        1 x composing: components.forms.tutor-subscription-join (0.02%)
        73μs
        1 x composing: components.forms.tutor-support (0.02%)
        71μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        58μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
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        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
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        1 x composing: site.layouts.app (0.01%)
        25μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
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      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
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      18 statements were executed, 3 of which were duplicates, 15 unique. Show only duplicated24.19ms
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        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
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        4.46mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
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        • 1: 0
        • 2: 33201
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (2)
        1.07mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (33201)
        990μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        990μstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 33201 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.19mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 33201
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 33201 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        800μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 33201
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
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        840μstwenty4_siteHomeworkLibrary.php#260
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
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        1.04mstwenty4_siteHomeworkLibrary.php#201
        Bindings
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        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
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        990μstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.08mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.05mstwenty4_siteSubject.php#100
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        2.65mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.18mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.08mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.05mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.22mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.23mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.28mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      6HomeworkLibraryFile.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      1HomeworkLibrary.php
      App\Models\Subject
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          status_text
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          request_cookies
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