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

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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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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