# Rates of change

• March 7th 2009, 04:06 AM
Orangeobe
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.
• March 7th 2009, 04:24 AM
running-gag
Hi

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