Question

I need help with my homework Please check work when done (Question 1)

Answer 1

The function representing the value of the car is given to be:

`C(t)=23746\cdot e^((rt))`

After 2 years, the value is $20,233. This means that:

`\begin{gathered} when \\ t=2,C(t)=20233 \end{gathered}`

Therefore, the value of r can be calculated to be:

`\begin{gathered} 20233=23746\cdot e^((2r)) \\ \mathrm{Divide\:both\:sides\:by\:}23746 \\ (23746e^(2r))/(23746)=(20233)/(23746) \\ e^(2r)=(20233)/(23746) \\ \text{Applying exponent rules} \\ 2r=\ln \left((20233)/(23746)\right) \\ r=(\ln\left((20233)/(23746)\right))/(2) \\ \therefore \\ r=-0.08 \end{gathered}`

Therefore, the function becomes:

`C(t)=23746\cdot e^(-0.08t)`

Therefore, after 7 years, the car's worth would be:

`\begin{gathered} At\text{ }t=7 \\ C(t)=23746\cdot e^(-0.08(7)) \\ C(t)\approx13,563.93 \end{gathered}`

Hence, the correct option is OPTION B.