Chapter 10.2, Problem 6E

Plutonium- $238$ is used as a compact source of electrical power in many applications. ranging from pace-makers to spacecraft. Suppose a power cell initially contains $1.6\text{ grams}$ of plutonium- $238$.

a. Develop the mathematical model that represents the amount of plutonium- $238$ present at time $t$.

b. Predict the amount of plutonium- $238$ remaining after one year.

c. Predict the amount of plutonium- $238$ remaining after $20\text{years}$.

d. Find $\Delta Q/\Delta t$, the average decay rate, for the first year.

e. Find $\left(\Delta Q/\Delta t\right)/Q$, the relative decay rate, for the first year.

f. Find $\Delta Q/\Delta t$, the average decay rate, for the first $20\text{year}$.

g. Find $\left(\Delta Q/\Delta t\right)/Q$, the relative decay rate, for the first $20\text{year}$.

h. Why is the absolute value of the answer to part (e) greater than the answer to part (g)?