
Rates of change
I'm having trouble fully understanding the following question. Can anyone help please?
p = e^(β0 + β1x) where β0 = 10.17 and β1 = 0.01581
dp/dx = β1e^(β0 + β1x)
The Question
A small change in mileage (x) will lead to a small change Δp in price.
They are related by the approximation:
Δp ≈ (dp/dx) Δx
Using this, derive an expression for the ratio of fractional change in price associated to a small change in mileage:
(Δp/p)/Δx
Hence find the percentage fall in price for every 1000 miles (x) travelled.

Hi
$\displaystyle \frac{\frac{\Delta p}{p}}{\Delta x} = \frac{1}{p}\:\frac{\Delta p}{\Delta x} = \frac{1}{p}\:\frac{dp}{dx} = \beta_1$