Question

PLSS HELP Find a formula for the exponential function passing through the points (-3, 3/8) and (3,24)

Answer 1

The exponential function is of the form:

`y=ab^x`

Given the two points, we can plug each point into the equation and see:

1.

`\begin{gathered} y=ab^x \\ (3)/(8)=ab^(-3) \end{gathered}`

2.

`\begin{gathered} y=ab^x \\ 24=ab^3 \end{gathered}`

Let's divide the the 2nd equation by the 1st one:

`\begin{gathered} (24)/((3)/(8))=(ab^3)/(ab^(-3)) \\ 24*(8)/(3)=(b^3)/(b^(-3)) \\ 64=b^(3+3) \\ b^6=64 \end{gathered}`

Note: we used the property of exponents, 1/a^x = a^ -x to simplify it.

Now, we can solve for b:

`\begin{gathered} b^6=64 \\ b=\sqrt[6]{64} \\ b=2 \end{gathered}`

The second equation, now, becomes:

`\begin{gathered} 24=ab^3 \\ 24=a(2)^3 \end{gathered}`

Now, we can easily find a:

`\begin{gathered} 24=a(8) \\ a=(24)/(8) \\ a=3 \end{gathered}`

We know b = 2 and a = 3.

So, the final equation will be:

`\begin{gathered} y=ab^x \\ y=3(2)^x \end{gathered}`