Chapter 4.6, Problem 25PE

The isotope of plutonium $\text{P}\text{u}$ is used to make thermoelectric power source, for spacecraft. Suppose that a space probe was launched in 2012 with 2.0 kg of $\text{P}\text{u}$.

a. If the half-life of $\text{P}\text{u}$ is 87.7 yr, write a function of the form $\text{Q}\left(t\right)=Q_0{e}^{-kt}$ to model the quantity $\text{Q}\left(t\right)$ of $\text{P}\text{u}$ left after t years.

b. If 1.6 kg of $\text{P}\text{u}$ is required to power the spacecraft’s data transmitter, for how long after launch would scientist be able to received data? Round to the nearest year.