Question

Find the formula for an exponential function that passes through the two points given.(x, y) = (0, 7) and (x, y) = (3, 56)f(x)=

Answer 1

The equation of an exponential function is of the form

`f(x)=a(b)^x`

we know that

For x=0 -----> f(x)=7

substitute

`\begin{gathered} 7=a(b)^0 \\ 7=a(1) \\ a=7 \end{gathered}`

substitute the value of a

`f(x)=7(b)^x`

Remember that

For x=3 ----> f(x)=56

substitute

`\begin{gathered} 56=7(b)^3 \\ b^3=(56)/(7) \\ \\ b^3=8 \\ b^3=2^3 \\ b=2 \end{gathered}`

The equation is given by

`f(x)=7(2)^x`