Question

The total attendance at a science museum is modeled by the function f(x)=14,788(1.025)x. If the initial total attendance (that is, the total attendance when x=0) was measured January 1, 2014, what will the total attendance be on January 1, 2030? Round your answer to the nearest whole number, if necessary.

Answer 1

SOLUTION:

Given that the attendance is modeled by;

$\begin{gathered} f(x)=14788(1.025)^x \\ \text{Where x is the time (years)} \end{gathered}$

At January 1, 2030, the value of x is;

$\begin{gathered} x=2030-2014 \\ x=16 \end{gathered}$

Thus, the total attendance on January 1, 2030 is;

$\begin{gathered} f(16)=14788(1.025)^{16} \\ f(16)=21952.87 \end{gathered}$

Then, the total attendance round to nearest whole number is;

$21,953\text{ people}$