Population growth with non-constant growth factor

I am dealing with a population with a characteristic growth rate of dp/dt = (a - p)/b per hour, where p is the current population, and a and b are constants. I am trying to derive a formula which, given a starting population, will tell me how long it will take to reach a target population. All of the formulas I can find assume that the growth rate can be calculated by applying a constant growth factor to the current population. I remember the basics of derivates and integrals but I'm having trouble figuring this one out. Can anyone help me out?