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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem

Radioactive Decay The rate of decomposition of radioactive einsteinium is proportional to the amount present at any time. The half-life of radioactive einsteinium is 276 days. After 100 days, 0.5 gram remains. What was the initial amount?

To determine

To calculate: The initial amount after 100 days, 0.5 grams remain.

Explanation

Given information:

The half-life of radioactive einsteinium is 276 years.

The rate of decomposition of radioactive einsteinium is proportional to the amount present at any time.

Formula Used:

Integration formula:

1ydy=ln|y|,kdt=kt+c

Calculation:

Let y represent the mass of the einsteinium and t represent the time in years.

According to question,

The rate of decomposition of radioactive einsteinium is proportional to the amount present at any time.

Therefore,

dydt=ky

Consider the differential equation,

dydt=ky

Separate the variable by grouping the t variable on side and the y variable on other side,

Therefore,

dydt=kydyy=kdt

Integrate each side of the above differential equation,

Therefore,

dyy=kdt

Apply, integration formula 1ydy=ln|y|,kdt=kt+c in dyy=kdt

Therefore,

dyy=kdtln|y|=

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Chapter 11 Solutions

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Sect-11.1 P-1ESect-11.1 P-2ESect-11.1 P-3ESect-11.1 P-4ESect-11.1 P-5ESect-11.1 P-6ESect-11.1 P-7ESect-11.1 P-8ESect-11.1 P-9ESect-11.1 P-10ESect-11.1 P-11ESect-11.1 P-12ESect-11.1 P-13ESect-11.1 P-14ESect-11.1 P-15ESect-11.1 P-16ESect-11.1 P-17ESect-11.1 P-18ESect-11.1 P-19ESect-11.1 P-20ESect-11.1 P-21ESect-11.1 P-22ESect-11.1 P-23ESect-11.1 P-24ESect-11.1 P-25ESect-11.1 P-26ESect-11.1 P-27ESect-11.1 P-28ESect-11.1 P-29ESect-11.1 P-30ESect-11.1 P-31ESect-11.1 P-32ESect-11.1 P-33ESect-11.1 P-34ESect-11.1 P-35ESect-11.1 P-36ESect-11.1 P-37ESect-11.1 P-38ESect-11.1 P-39ESect-11.1 P-40ESect-11.1 P-41ESect-11.1 P-42ESect-11.1 P-43ESect-11.1 P-44ESect-11.1 P-45ESect-11.1 P-46ESect-11.2 P-1CPSect-11.2 P-2CPSect-11.2 P-3CPSect-11.2 P-4CPSect-11.2 P-5CPSect-11.2 P-6CPSect-11.2 P-1SWUSect-11.2 P-2SWUSect-11.2 P-3SWUSect-11.2 P-4SWUSect-11.2 P-5SWUSect-11.2 P-6SWUSect-11.2 P-7SWUSect-11.2 P-8SWUSect-11.2 P-9SWUSect-11.2 P-10SWUSect-11.2 P-1ESect-11.2 P-2ESect-11.2 P-3ESect-11.2 P-4ESect-11.2 P-5ESect-11.2 P-6ESect-11.2 P-7ESect-11.2 P-8ESect-11.2 P-9ESect-11.2 P-10ESect-11.2 P-11ESect-11.2 P-12ESect-11.2 P-13ESect-11.2 P-14ESect-11.2 P-15ESect-11.2 P-16ESect-11.2 P-17ESect-11.2 P-18ESect-11.2 P-19ESect-11.2 P-20ESect-11.2 P-21ESect-11.2 P-22ESect-11.2 P-23ESect-11.2 P-24ESect-11.2 P-25ESect-11.2 P-26ESect-11.2 P-27ESect-11.2 P-28ESect-11.2 P-29ESect-11.2 P-30ESect-11.2 P-31ESect-11.2 P-32ESect-11.2 P-33ESect-11.2 P-34ESect-11.2 P-35ESect-11.2 P-36ESect-11.2 P-37ESect-11.2 P-38ESect-11.2 P-39ESect-11.2 P-40ESect-11.2 P-41ESect-11.2 P-42ESect-11.2 P-43ESect-11.2 P-44ESect-11.2 P-45ESect-11.2 P-46ESect-11.2 P-47ESect-11.2 P-1QYSect-11.2 P-2QYSect-11.2 P-3QYSect-11.2 P-4QYSect-11.2 P-5QYSect-11.2 P-6QYSect-11.2 P-7QYSect-11.2 P-8QYSect-11.2 P-9QYSect-11.2 P-10QYSect-11.2 P-11QYSect-11.2 P-12QYSect-11.2 P-13QYSect-11.2 P-14QYSect-11.2 P-15QYSect-11.2 P-16QYSect-11.3 P-1CPSect-11.3 P-2CPSect-11.3 P-3CPSect-11.3 P-1SWUSect-11.3 P-2SWUSect-11.3 P-3SWUSect-11.3 P-4SWUSect-11.3 P-5SWUSect-11.3 P-6SWUSect-11.3 P-7SWUSect-11.3 P-8SWUSect-11.3 P-9SWUSect-11.3 P-10SWUSect-11.3 P-1ESect-11.3 P-2ESect-11.3 P-3ESect-11.3 P-4ESect-11.3 P-5ESect-11.3 P-6ESect-11.3 P-7ESect-11.3 P-8ESect-11.3 P-9ESect-11.3 P-10ESect-11.3 P-11ESect-11.3 P-12ESect-11.3 P-13ESect-11.3 P-14ESect-11.3 P-15ESect-11.3 P-16ESect-11.3 P-17ESect-11.3 P-18ESect-11.3 P-19ESect-11.3 P-20ESect-11.3 P-21ESect-11.3 P-22ESect-11.3 P-23ESect-11.3 P-24ESect-11.3 P-25ESect-11.3 P-26ESect-11.3 P-27ESect-11.3 P-28ESect-11.3 P-29ESect-11.3 P-30ESect-11.3 P-31ESect-11.3 P-32ESect-11.3 P-33ESect-11.3 P-34ESect-11.3 P-35ESect-11.3 P-36ESect-11.3 P-37ESect-11.3 P-38ESect-11.3 P-39ESect-11.3 P-40ESect-11.4 P-1CPSect-11.4 P-2CPSect-11.4 P-3CPSect-11.4 P-4CPSect-11.4 P-5CPSect-11.4 P-1SWUSect-11.4 P-2SWUSect-11.4 P-3SWUSect-11.4 P-4SWUSect-11.4 P-5SWUSect-11.4 P-6SWUSect-11.4 P-7SWUSect-11.4 P-8SWUSect-11.4 P-9SWUSect-11.4 P-10SWUSect-11.4 P-1ESect-11.4 P-2ESect-11.4 P-3ESect-11.4 P-4ESect-11.4 P-5ESect-11.4 P-6ESect-11.4 P-7ESect-11.4 P-8ESect-11.4 P-9ESect-11.4 P-10ESect-11.4 P-11ESect-11.4 P-12ESect-11.4 P-13ESect-11.4 P-14ESect-11.4 P-15ESect-11.4 P-16ESect-11.4 P-17ESect-11.4 P-18ESect-11.4 P-19ESect-11.4 P-20ESect-11.4 P-21ESect-11.4 P-22ESect-11.4 P-23ESect-11.4 P-24ESect-11.4 P-27ESect-11.4 P-28ESect-11.4 P-29ESect-11.4 P-30ESect-11.4 P-31ESect-11.4 P-32ESect-11.4 P-33ESect-11.4 P-34ESect-11.4 P-35ESect-11.4 P-36ESect-11.4 P-37ESect-11.4 P-38ECh-11 P-1RECh-11 P-2RECh-11 P-3RECh-11 P-4RECh-11 P-5RECh-11 P-6RECh-11 P-7RECh-11 P-8RECh-11 P-9RECh-11 P-10RECh-11 P-11RECh-11 P-12RECh-11 P-13RECh-11 P-14RECh-11 P-15RECh-11 P-16RECh-11 P-17RECh-11 P-18RECh-11 P-19RECh-11 P-20RECh-11 P-21RECh-11 P-22RECh-11 P-23RECh-11 P-24RECh-11 P-25RECh-11 P-26RECh-11 P-27RECh-11 P-28RECh-11 P-29RECh-11 P-30RECh-11 P-31RECh-11 P-32RECh-11 P-33RECh-11 P-34RECh-11 P-35RECh-11 P-36RECh-11 P-37RECh-11 P-38RECh-11 P-39RECh-11 P-40RECh-11 P-41RECh-11 P-42RECh-11 P-43RECh-11 P-44RECh-11 P-45RECh-11 P-46RECh-11 P-47RECh-11 P-48RECh-11 P-49RECh-11 P-50RECh-11 P-51RECh-11 P-52RECh-11 P-53RECh-11 P-54RECh-11 P-55RECh-11 P-56RECh-11 P-57RECh-11 P-58RECh-11 P-59RECh-11 P-60RECh-11 P-61RECh-11 P-62RECh-11 P-63RECh-11 P-64RECh-11 P-65RECh-11 P-66RECh-11 P-67RECh-11 P-68RECh-11 P-69RECh-11 P-70RECh-11 P-71RECh-11 P-72RECh-11 P-73RECh-11 P-74RECh-11 P-75RECh-11 P-76RECh-11 P-77RECh-11 P-1TYSCh-11 P-2TYSCh-11 P-3TYSCh-11 P-4TYSCh-11 P-5TYSCh-11 P-6TYSCh-11 P-7TYSCh-11 P-8TYSCh-11 P-9TYSCh-11 P-10TYSCh-11 P-11TYSCh-11 P-12TYSCh-11 P-13TYS

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