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 price of the item and let x be the number of years after the initial value. In this case, the initial value is a price of $4.50. Since the price increases 3.5 % each year, we have that r=0.035.
y=4.5 [ 1+0.035]^x
⇕
y=4.5 ( 1.035)^x
