Question

The table shows the number of books donated to a library each month. Suppose the growth continues exponentially.

Answer 1

$\bf \begin{array}{ccll} \stackrel{t}{months}&\stackrel{A}{books}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 0&80\\ 1&100\\ 2&125 \end{array}$,    we know that on Month 0, the Books were 80

$\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &80\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\to &0\\ \end{cases} \\\\\\ 80=I(1+r)^0\implies 80=I\qquad therefore\qquad \boxed{A=80(1+r)^t}$

we also know that on the first month there were 100 books,

$\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &100\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\to &1\\ \end{cases} \\\\\\ 100=80(1+r)^1\implies \cfrac{100}{80}=1+r\implies \cfrac{5}{4}=1+r \implies \cfrac{5}{4}-1=r \\\\\\ \cfrac{1}{4}=r\implies 0.25=r\qquad therefore\qquad \boxed{A=80(1+0.25)^t}$

now, how many books when t = 8?   A=80(1+0.25)⁸, or A=80(1.25)⁸.

Answer 2

Hello, The answer to this problem is 477

How i got it;

Well were using the formula

A(t)=b(1+r)^t

Now all we have to do it fill in the blanks.

So when doing so its A=80(1+0.25)^t

t=8

1+.25=1.25

A=80(1.25)^8

Not do the math and theirs your answer!

Answer: 476.837 rounded to 477

Hope this helps!