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 value of the sound system and x be the number of years after the initial value. In this case, the initial value is a price of $900. Since the value decreases 9 % each year, we have that r=- 0.09.
y=900 [ 1+(- 0.09)]^x
⇕
y=900 ( 0.91)^x
