The value, $V$ dollars, of a second-hand vehicle depreciates over time. Given that \(V=153000

Question

The value, $V$ dollars, of a second-hand vehicle depreciates over time. Given that $V=153000{{\mathrm e}^{dt}}$, where $t$ is the time in years since it was bought and $d$ is the constant of depreciation. Calculate the initial value of the vehicle, the value of $d$, if after 3 years, the value of the vehicle dropped by one-third of its initial value. the value of $t$ when the value of the vehicle is one-sixth its original value.

Accepted Answer

(a) $V = \$153,000$ (b) $d = \frac{1}{3}\ln\left(\frac{2}{3}\right)$ or $-0.135$ (3 s.f.) (c) $t = 13.3$ years (3 s.f.)

Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions

Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions

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