Question

The value of a car when new is R224 000,00. It is estimated that the value of the car will decrease at the

rate of 11% per year. Answer the following questions:

a. Determine the exponential function that describes the value of the car y years after it was bought.

b. Determine the value of the car six years after it was bought.

Answer 1

a. The rate of decrease is −0.11, and this can be written as 1−0.11=0.89.

An exponential function is of the form of $P=A\cdot r^t,$ where A is the initial value, r is the rate of increase/decrease in decimals, t - time in years.

The equation is hence $P=224000\cdot 0.89^t.$

b. We substitute t=6 into the function, and that will give us:

$P(6)=224000\cdot 0.89^6=\text{R}111\ 323.81.$