Edexcel C34 2015 January — Question 8

Exam BoardEdexcel
ModuleC34 (Core Mathematics 3 & 4)
Year2015
SessionJanuary
TopicExponential Functions

8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{03548211-79cb-4629-b6ca-aa9dfcc77a33-13_743_1198_219_372} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} The value of Lin's car is modelled by the formula $$V = 18000 \mathrm { e } ^ { - 0.2 t } + 4000 \mathrm { e } ^ { - 0.1 t } + 1000 , \quad t \geqslant 0$$ where the value of the car is \(V\) pounds when the age of the car is \(t\) years.
A sketch of \(t\) against \(V\) is shown in Figure 1.
  1. State the range of \(V\). According to this model,
  2. find the rate at which the value of the car is decreasing when \(t = 10\) Give your answer in pounds per year.
  3. Calculate the exact value of \(t\) when \(V = 15000\)