Solving Initial Value Problem for Exponential Growth

[Precursor]

Homework Statement
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?

 

[jbunniii]

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