Mr Phua bought a new car. After $t$ months, its value $V$ is given by \(V = 250 \ 000 \mathrm{e}

Question

Mr Phua bought a new car. After $t$ months, its value $V$ is given by $V = 250 \ 000 \mathrm{e}^{-pt}$, where $p$ is a constant. The value of the car after $36$ months is $180 \ 000$. Show that $p$ is approximately $0.00913$.[2] Calculate the age of the car, to the nearest month, when its expected value will be $100 \ 000$.[2] $5$ years after Mr Phua bought the car, a second-hand car agent offers to pay him $130 \ 000$ for his car. Would you advise Mr Phua to take up the offer. Explain your answer.[2] Sketch the graph of $V = 250 \ 000 \mathrm{e}^{-pt}$, for $t \ge 0$.[2]

Accepted Answer

(a) $p\approx0.00913$ (3 s.f.) (b) $100$ months (nearest month) (c) Decline: the predicted value is approximately $\$145\,000$ (3 s.f.), above $\$130\,000$. (d) Decreasing curve from $(0,250\,000)$, with horizontal asymptote $V=0$.

2024 GESS PRELIMS P2 Q2

2024 GESS PRELIMS P2 Q2

Solution:

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