Question

Sales representatives of a new line of computers predict that sales can be approximated by the function S(t) = 1200 + 540\n(31 + e),where t is measured in years. What are the predicted sales in 13 years? Round your answer to the nearest whole number.

Answer 1

We have the function

$S(t)=1200+540\ln(31t+e)$

And we want to evaluate S(13), therefore

$\begin{gathered} S(13)=1200+540\ln(31\cdot13+e) \\ \\ S(13)=1200+540\operatorname{\ln}(403+e) \\ \\ \end{gathered}$

Here we must use a calculator to get the result

$\begin{gathered} S(13)=1200+540\operatorname{\ln}(403+e) \\ \\ S(13)=1200+540\cdot6.00566 \\ \\ S(13)=1200+3243.05587 \\ \\ S(13)=4443.05587708 \\ \\ S(13)=4443 \end{gathered}$

The predicted sales in 13 years are 4443 computers