Question

If f(c) is an exponential function where f(3) = 11and f(11) = 63, then find the value of f(6), to the nearest hundredth.

Answer 1

The general form of an exponential function is,

`f(x)=ab^x`

Given that f(3)=11 and f(11)=63 implies,

`\begin{gathered} 11=ab^3\ldots\ldots(1) \\ 63=ab^(11)\ldots\ldots(2) \end{gathered}`

Divide equation (2) by (1) implies,

`\begin{gathered} (63)/(11)=b^8 \\ b=1.24 \end{gathered}`

Then, the value of a is,

`\begin{gathered} 11=a*1.24^3 \\ a=5.76 \end{gathered}`

Therefore, the function is,

`f(x)=5.76*1.24^x`

Find the value of f(6).

`\begin{gathered} f(6)=5.76*1.24^6 \\ =20.93 \end{gathered}`

Therefore, the answer is 20.93