In a galaxy far, far away (my professor writes his own practice problems), on the planet Xylor, a herd of 100 Tybars was introduced for breeding. After 5 years, the herd had increased to 500. If the rate of herd growth is assumed to be directly proportional to the number of Tybars present on Xylor at any time t:
a. How many Tybars would be found on Xylor after 5 more years have passed?
b. It is conjectured that the maximum number of Tybars that could be sustained on the planet is 312,500. How many years from the date of introduction of the herd will it take for the number of Tybars to reach that number?
We know that the rate of herd growth is assumed to be directly proportional to the number of Tybars present on Xylor at any time t: This means that we have an equation of the form
dP/dt = kP
where P is the population and t is the time (k is a constant that we put in to make the rate proportional to, but not necessarily equal to, the current population). We also know that at year t = 0, P = 100, and after 5 years ...
The solution shows how to solve two problems related to population/exponential growth.