Question

Annual sales of a certain brand of phone are expected to grow at the rate off' (t) = 0.18t^2+ 0.16t+ 2.64million phones per year. Use a definite integral to determine the total number of phones that will be sold over the next 10 years.

Answer 1

Given the Annual sales of a certain brand of phones are expected to grow at the rate of:

$f^{\prime}(t)=0.18t^2+0.16t+2.64$

We will use the definite integral to determine the total number of phones that will be sold over the next 10 years.

$\begin{gathered} \int f^{\prime}(t)=\int ^{10}_00.18t^2+0.16t+2.64 \\ \\ =(\frac{0.18}{3}t^3+\frac{0.16}{2}t^2+2.64t)|^{10} \\ \\ =0.06\cdot10^3+0.08\cdot10^2+2.64\cdot10 \\ =94.4 \end{gathered}$

So, the answer will be the number of phones = 94.4 million phones