3 Exponential decrease

Consider the value, $\pounds D$ , of a car subject to depreciation, in terms of the age $A$ years of the car. The car was bought for $\pounds 10500$ . The function

$D=10500e^{-0.25A}\left(0\le A\le 6\right)$

could be considered appropriate on the ground that

1. $D$ had a fixed value of $\pounds 10500$ when

   $A$ = 0,

2. $D$ decreases as $A$ increases and
3. $D$ decreases faster when $A$ is small than when $A$ is large. A plot of this function is shown in Figure 8.

   Figure 8 :

   

Task!

Produce the linearised model of $D=10500e^{-0.25A}$ .

Answer