Consider the given expression,
[tex]y=82(1.045)^x[/tex]The first derivative gives the rate of growth for the number of followers.
Solve for the first derivative as,
[tex]\begin{gathered} \frac{dy}{dx}=82\times\frac{d \square}{dx}(1.045)^x \\ \frac{dy}{dx}=82\times(1.045)^x\ln (1.045) \\ \frac{dy}{dx}=y\times0.045 \\ \frac{dy}{dx}=4.5\text{ percent of y} \end{gathered}[/tex]Thus, the rate of growth of followers is approximately 4.5% each week.
Therefore, option C is the correct choice.
The number of followers corresponding to the 4th week is calculated as,
[tex]y=82\times(1.045)^4=82\times1.1925=97.7865\approx98[/tex]Thus, Michael should expect approximately 98 followers in 4th week.