Question

The tuition at a local community college was ​$1685 in 1992 and​ $2392 in 1997. Find the rate at which tuition was increasing.

Answer 1

So, from 1992 to 1997, it went up by some "r" rate, ok.. that means some percentage, that means some rate of growth, so is an exponential function, with a positive rate, or +r

if we take 1992, to be 0years, then the starting amount for the tuition is 1685

that is    $\bf A=P\left(1+r\right)^t \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{starting amount}\to &\ 1685\\ r=rate\\ t=years\to &0 \end{cases} \\\\\\ A=1685\left(1+r\right)^0\implies A=1685\cdot 1\implies A=1685$

now, let's go to 1997, 5 years later, when t = 5, we know the tuition price then was 2392, so A = 2392

thus   $\bf A=P\left(1+r\right)^t \quad \begin{cases} A=\textit{accumulated amount}\to &\ 2392\\ P=\textit{starting amount}\to &\ 1685\\ r=rate\\ t=years\to &5 \end{cases} \\\\\\ 2392=1685(1+r)^5\implies \cfrac{2392}{1685}=(1+r)^5\implies \sqrt[5]{\cfrac{2392}{1685}}=1+r \\\\\\ \boxed{\sqrt[5]{\cfrac{2392}{1685}}-1=r}$

now, you'd get a value in decimal format, so, to get the % format, simply multiply it by 100