Answer :
Answer: 5.2 years, $5.28
Step-by-step explanation:
Given
The value of a car is given by [tex]y=24,000\left(0.845\rght)^t[/tex]
Substitute [tex]\$10,000[/tex] for [tex]y[/tex]
[tex]\Rightarrow 10,000=24,000\left(0.845\right)^t\\\\\Rightarrow \left(0.845\right)^t=\dfrac{5}{12}\\\\\Rightarrow \left(0.845\right)^t=0.41666\\\text{Taking log both sides}\\\Rightarrow t\ln (0.845)=\ln (0.4166)\\\\\Rightarrow t=\dfrac{\ln 0.4167}{\ln 0.845}\\\\\Rightarrow t=5.197\approx 5.2\ \text{years}[/tex]
(b) After 50 years, it is
[tex]\Rightarrow y=24,000\left(0.845\rght)^{50}[/tex]
[tex]\Rightarrow y=24,000\times 0.00022\\\Rightarrow y=\$5.28[/tex]
No, this is not a reasonable value as it is more than 4000 times less.