To write an exponential function to model the given situation, let's first recall the general form of an exponential equation.
y=a b^x
In this formula a is the initial value and b= 1+r, where r is the rate of change. If the function represents growth, then r> 0. If it represents decay, then r<0.
Writing the Equation
To write the function we first need to define the variables. Let y be the sales, and let x be the number of years after the initial value. In this case the initial value is $10 000. Since the price increases 65 % each year, we have that r=0.65.
y=10 000 [ 1+0.65]^x
⇕
y=10 000 ( 1.65)^x
