Answer:
If one of the data points has the form \displaystyle \left(0,a\right)(0,a), then a is the initial value. Using a, substitute the second point into the equation \displaystyle f\left(x\right)=a{\left(b\right)}^{x}f(x)=a(b)
x
, and solve for b.
If neither of the data points have the form \displaystyle \left(0,a\right)(0,a), substitute both points into two equations with the form \displaystyle f\left(x\right)=a{\left(b\right)}^{x}f(x)=a(b)
x
. Solve the resulting system of two equations in two unknowns to find a and b.
Using the a and b found in the steps above, write the exponential function in the form \displaystyle f\left(x\right)=a{\left(b\right)}^{x}f(x)=a(b)
x
.
Step-by-step explanation:
