Question

Write an exponential function in the form y and (2,171). ab that goes through points (0,19)

Answer 1

The exponential function has the following form:

`y=a\cdot b^x`

The function goes through the points ( 0, 19) and ( 2, 171 )

We will use the points to find the values of a and b

`\begin{gathered} x=0\rightarrow y=19 \\ \\ 19=a\cdot b^0 \\ b^0=1 \\ a=19 \end{gathered}`

Substitute with the point ( 2, 171 ) and the value of a to find b

`\begin{gathered} x=2\rightarrow y=171 \\ a=19 \\ \\ 171=19\cdot b^2 \\ \\ b^2=(171)/(19)=9 \\ \\ b=\sqrt[]{9}=3 \end{gathered}`

So, the answer will be:

`y=19\cdot3^x`