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 :

Average Rate of Change.

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

The average rate of change is given by;

[tex]\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}[/tex][tex]m(2)=126(0.84)^2=\text{ 88.906}[/tex][tex]\text{Average Rate of Change =}\frac{m(5)\text{ - m(2)}}{5\text{ - 2}}=\frac{52.695-88.906}{5-2}=\frac{-36.211}{3}=-12.070\text{ }\approx-12.1\text{ grams per year}[/tex]

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

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