The general exponential function is,
[tex]f(x)=a\cdot(b)^x[/tex]
For x = 0, f(x) = 80. So,
[tex]\begin{gathered} 80=a\cdot(b)^0 \\ 80=a\cdot1 \\ a=80 \end{gathered}[/tex]
For x = 1, f(x) = 100 and a = 80. So,
[tex]\begin{gathered} 100=80\cdot(b)^1 \\ b=\frac{100}{80} \\ =1.25 \end{gathered}[/tex]
So exponential function is,
[tex]f(x)=80\cdot(1.25)^x[/tex]
Substitute 8 for x in the function to determine the number of books in 8th month.
[tex]\begin{gathered} f(8)=80\cdot(1.25)^8 \\ =476.83 \\ \approx477 \end{gathered}[/tex]
So in 8th month number of book denoted is 477.
