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denis-greek [22]

3 years ago

10

Mia borrowed 5,000 from her grandparents to pay college expenses. She pays them 125 each month,and simple interest at an annual

rate of 5% on the remaining valence of the loan at the end of the year?
How many months will it take her to pay the loan off? Explain.

1 answer:

ivanzaharov [21]3 years ago

8 0

It will take her 40 months

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Every two years, a manufacturer's total yearly sales decline 20%. She sells 400 total units in her first year. Rounded to the ne

Vesna [10]

$\bf \textit{Periodic Exponential Decay}\\\\
A=I(1 - r)^{\frac{t}{p}}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\\
p=period
\end{cases}$

we know, the first year she sold 400 units, thus year 0, 400 units, t = 0, A = 400.

$\bf \textit{Periodic Exponential Decay}\\\\
A=I(1 - r)^{\frac{t}{p}}\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &400\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\to &0\\
p=period
\end{cases}
\\\\\\
400=I(1-r)^{\frac{0}{p}}\implies 400=I\cdot 1\implies 400=I$

therefore then

$\bf \textit{Periodic Exponential Decay}\\\\
A=I(1 - r)^{\frac{t}{p}}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\to &400\\
r=rate\to 20\%\to \frac{20}{100}\to &0.20\\
t=\textit{elapsed time}\\
p=period\to &2
\end{cases}
\\\\\\
A=400(1-0.2)^{\frac{t}{2}}$

now, how many units will it had decreased by the 9th year? t = 9

$\bf A=400(1-0.2)^{\frac{9}{2}}$

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