Question

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

How many books were donated to the library in Month 8?

Round to the nearest whole number.

Enter your answer in the box. ____

Month 0 1 2
Number of books 80 100 125

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 (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 (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!