Question

The number of subscribers y to a website after t years is shown by the equation below:

y = 50(1.75)t

Which conclusion is correct about the number of subscribers to the website?
It increased by 75% every year.
It decreased by 75% every year.
It increased by 50% every year.
It decreased by 50% every year.

Answer 1

$\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time} \end{cases}\\\\ -------------------------------\\\\ y=50(1.75)^t\implies \begin{array}{llllll} y=&50(&1+&0.75)&^t\\ \uparrow &\uparrow &&\uparrow &\uparrow \\ A&I&&r&t \end{array}\qquad \cfrac{r}{100}=0.75 \\\\\\ r=100\cdot 0.75\implies \boxed{r=75\%}$

the amount is a positive "r", rate, thus is a growth equation, so it increased.

Answer 2

Answer: A. It increased by 75% every year.