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.

Answer 1

The general exponential function is,

`f(x)=a\cdot(b)^x`

For x = 0, f(x) = 80. So,

`\begin{gathered} 80=a\cdot(b)^0 \\ 80=a\cdot1 \\ a=80 \end{gathered}`

For x = 1, f(x) = 100 and a = 80. So,

`\begin{gathered} 100=80\cdot(b)^1 \\ b=(100)/(80) \\ =1.25 \end{gathered}`

So exponential function is,

`f(x)=80\cdot(1.25)^x`

Substitute 8 for x in the function to determine the number of books in 8th month.

`\begin{gathered} f(8)=80\cdot(1.25)^8 \\ =476.83 \\ \approx477 \end{gathered}`

So in 8th month number of book denoted is 477.