Question

a radioactive material has a mass given by m(t)= 126(0.84)^t, where the mass is in grams and the time , t is in years which of the following gives the average rate of change of the mass over the interval 2

Answer 1

Average Rate of Change.

The correct answer is -12.1 grams per year (option 1)

The average rate of change is given by;

`\begin{gathered} \text{Average Rate of Change =}\frac{m(5)\text{ - m(2)}}{5\text{ - 2}} \\ \text{Where m(5) =}126(0.84)^5=\text{ 52.695} \end{gathered}`
`m(2)=126(0.84)^2=\text{ 88.906}`
`\text{Average Rate of Change =}\frac{m(5)\text{ - m(2)}}{5\text{ - 2}}=(52.695-88.906)/(5-2)=(-36.211)/(3)=-12.070\text{ }\approx-12.1\text{ grams per year}`

So, the correct answer is -12.1 grams per year (option 1)