Problem
As a car ages, its value decreases. The value of a particular car with an original purchase price of $\$ 24,100$ is modeled by the following function, where $c$ is the value at time $t$, in years. \[ c(t)=24,100(1-0.23)^{t} \] a. What is the value of the car when it is 2 years old? The value of the car after 2 years is $\$$ $\sigma^{8}$ b. What is the total depreciation amount after 3 years? After 3 years, the total depreciation amount is $\$$
Solution
Step 1 ：Given the function for the value of the car, \(c(t)=24,100(1-0.23)^{t}\), where \(c\) is the value at time \(t\), in years.
Step 2 ：We are asked to find the value of the car when it is 2 years old. This can be calculated by substitifying \(t=2\) into the given function.
Step 3 ：Calculating \(c(2)=24,100(1-0.23)^{2}\), we get the value of the car after 2 years.
Step 4 ：Final Answer: The value of the car when it is 2 years old is \(\boxed{14288.89}\).
