Question

Write an exponential function that models this situation. Let x represent the number of years since 2010 and let f(x)represent the number of lions.

Answer 1

`f(x)=2(4)^x`

Explanations:

The standard exponential function is given as:

`y=ab^x`

Given the coordinate points (2, 32) and (3, 128)

The two exponential functions will be;

`\begin{gathered} y_1=ab^(x_1) \\ y_2=ab^(x_2) \\ \end{gathered}`

Substitute the given coordinates to have:

`\begin{gathered} 32=ab^2 \\ 128=ab^3 \end{gathered}`

Divide both expressions to have:

`\begin{gathered} (128)/(32)=(ab^3)/(ab^2) \\ b^(3-2)=4 \\ b=4 \end{gathered}`

Determine the value of "a"

`\begin{gathered} 32=ab^2 \\ 32=a(4)^2 \\ 32=16a \\ a=2 \end{gathered}`

Substitute b = 4 and a = 2 into the original equation to have;

`\begin{gathered} y=ab^x \\ y=2(4)^x \\ f(x)=2(4)^x \end{gathered}`

This gives the required exponential function