# Exponential growth

1. Mar 14, 2010

### Precursor

The problem statement, all variables and given/known data
To encourage buyers to place 100-unit orders, your firm's sales department applies a continuous discount that makes the unit price a function p(x) of the number of units x ordered. The discount decreases the price at a rate of $0.01 per unit ordered. The price per unit for a 100-unit order is p(100) =$20.09. Find p(x) by solving the following initial value problem:

Differential equation: dp/dx = -p/100
Initial condition: p(100) = 20.09

The attempt at a solution
So I integrated the differential equation and applied the initial condition to it. I was able to get the following equation:

$$p = 20.09e^{1 - x/100}$$

Is this correct?

Last edited: Mar 14, 2010
2. Mar 14, 2010

### jbunniii

Yes, it's correct. You can verify it by confirming that it satisfies the differential equation and the initial condition.