ANSWER
It will take 13 years.
EXPLANATION
First, we have to write the equation that represents the situation.
It is a depreciation, which means that it is a compound decrease.
Compound decrease is generally given as:
[tex]\begin{gathered} A=P(1-r)^t \\ A=\text{amount;} \\ P=\text{initial amount} \\ r=\text{rate} \\ t=\text{amount of time} \end{gathered}[/tex]
Therefore, from the question:
[tex]\begin{gathered} A=95000(1-\frac{6.25}{100})^t=90000(1-0.0625)^t \\ A=95000(0.9375)^t \end{gathered}[/tex]
To find the number of years after which the boat will have a value of $40,000, we have to find t when A is $40,000.
That is:
[tex]\begin{gathered} 40000=95000(0.9375)^t \\ \text{Divide both sides by 95000:} \\ \frac{40000}{95000}=0.9375^t \\ 0.42=0.9375^t \\ Find\text{ the log of both sides:} \\ \log (0.42)=\log (0.9375)^t=t\cdot\log (0.9375) \\ D\text{ivide both sides by log(0.9375)}\colon \\ t=\frac{\log(0.42)}{\log(0.9375)} \\ t\approx13\text{ years} \end{gathered}[/tex]
It will babout 13 years for the value for the value of the car to be $40,000.
