Mathematics
06.01.2021 12:02
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The tuition at a local community college was $1685 in 1992 and $2392 in 1997. find

The tuition at a local community college was $1685 in 1992 and $2392 in 1997. find the rate at which tuition was increasing.
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srl63
srl63
4,9(41 marks)
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
sainijasdeep27
sainijasdeep27
4,4(80 marks)

Step-by-step explanation:

vertex-form equation for a vertical parabola with vertex (h,k):

y = a(x-h)² + k

y = -1.5(x+2)²

vertex (-2,0)

y-intercept = -1.5(0+2)² = -6

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