75% of a quantity of U-232 remains after 30 years. What is the half life? 200 YEALS6.7590 OFA QUANTITY OFU-232 REMAIUS AFTER30 YEARS. WHAT IS THE HALF UFÆ?つ-x-8x-S

The quantity remains after 30 years is 75%. It is given that AA0=0.75 , t=30 years. The equation…

Answered: antity of U-232 remains after 30 yea

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Calculus

antity of U-232 remains after 30 yea

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter7: Percents

Section7.7: Simple And Compound Interest

Problem 5E

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Question

75% of a quantity of U-232 remains after 30 years. What is the half life?

200 YEALS
6.7590 OFA QUANTITY OFU-232 REMAIUS AFTER
30 YEARS. WHAT IS THE HALF UFÆ?
つ-x-8x-S

Expert Solution

Step 1

The quantity remains after 30 years is 75%.

It is given that $\frac{A}{A_{0}} = 0.75$ , $t = 30 y e a r s .$

The equation represents

$\begin{array}{rcl} \frac{A}{A_{0}} & = & e^{- λ t} \\ 0.75 & = & e^{- λ \times 30} \\ \ln 0.75 & = & - 30 λ \ln e \\ λ & = & \frac{\ln 0.75}{- 30} \\ = & 9.6 \times 10^{- 3} \end{array}$

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