Question

suppose g is an exponential function and g(2)=33.5359 and g(3)= 33.603. write a function formula for gg(x)= ?

Answer 1

If g is an exponential function, it has the form:

`g(x)=a\cdot b^x`

We know two values of the function, and we will use them to find a and b.

We start by finding b, as we have:

`\begin{gathered} (g(3))/(g(2))=(ab^3)/(ab^2)=b^(3-2)=b \\ b=(g(3))/(g(2))=(33.603)/(33.5359)\approx1.0002 \end{gathered}`

Then, we use one of the points to find a:

`\begin{gathered} g(3)=a\cdot1.0002^3=33.603 \\ a=(33.603)/(1.0002^3)\approx(33.603)/(1.0006)\approx33.583 \end{gathered}`

We can then write g(x) as:

`g(x)=33.583\cdot1.0002^x`