Question

write an equation for the exponential function that includes that pair of given points. (1,12) and (-1,0.75)

Answer 1

Given:

The points of the exponential function are (1,12) and (-1,0.75).

The objective is to write the equation of the exponential function.

Step-by-step explanation:

The general equation of exponential is,

`y=a(b)^x\text{ . . . . . .(1),}`

First, substitute (1,12) in equation (1).

`\begin{gathered} 12=a(b)^1 \\ 12=ab\text{ . . . . . .(2)} \end{gathered}`

Now, substitute (-1,0.75) in equation (1).

`\begin{gathered} 0.75=a(b)^(-1) \\ 0.75=(a)/(b) \\ 0.75b=a\ldots\text{.}\mathrm{}(3) \end{gathered}`

To find b:

Substitute the value of an in equation (2).

`\begin{gathered} 12=(0.75b)(b) \\ (12)/(0.75)=b^2 \\ 16=b^2 \\ \sqrt[]{16}=b \\ b=4 \end{gathered}`

To find a:

Substitute the value of b in equation (3),

`\begin{gathered} 0.75(4)=a \\ a=3 \end{gathered}`

To find the equation:

Substitute the value of a and b in equation (1).

`y=3(4)^x`

Hence, the equation of the exponential function is y = 3(4)^x.e