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 :

The equation of an exponential function is of the form

[tex]f(x)=a(b)^x[/tex]

we know that

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

substitute

[tex]\begin{gathered} 7=a(b)^0 \\ 7=a(1) \\ a=7 \end{gathered}[/tex]

substitute the value of a

[tex]f(x)=7(b)^x[/tex]

Remember that

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

substitute

[tex]\begin{gathered} 56=7(b)^3 \\ b^3=\frac{56}{7} \\ \\ b^3=8 \\ b^3=2^3 \\ b=2 \end{gathered}[/tex]

The equation is given by

[tex]f(x)=7(2)^x[/tex]