Malthus' Principle of Population Growth: Solving a Differential Equation

[notme]

Malthus' principle of population growth can be written as the differential equation

y'=ky

where y(t) is the population t years after the initial measurement and k is the growth constant. The solution to this differential equation is given by

y(t)=Ae^{kt}

where A is the initial amount. If k = 0.03, determine the annual percent increase in y.

The % of increse changes every year... I don't know what to do.

 

[HallsofIvy]

If the population is A this year, according to your equation, it should be Ae^k next year. How great an increase is that? What percentage of the original population is that increase? The whole point of this problem is that while the amount of increase changes every year, the percentage of increase does NOT!