Additional Review Problems

Diff EQ Quest

Exponential GrowthIn a certain country the number of jobs

created is proportional to the number of people who already have jobs. If there are 15 million people who have jobs at time t = 0, and 15.1 million people with jobs 3 months later, how many jobs will exist in two years?

Exponential Growthf(t) = number of people with jobs at time t

monthsf’(t) = k f(t) for some constant tGiven f(0) = 15, then f(t) = 15ekt

Given f(3) = 15.1, then k = 0.002215At 24 months, f(24) = 15.8 million jobs

Population ProblemA certain population of critters C(t) increases

at a rate directly proportional to 2000 – C(t) when t > 0.

If C(0) = 1800, find C(t) in terms of t and a constant k.

If C(5) = 1750, find C(20)

SolutionC(t) = 2000 – 200e-kt

k = -.044629

C(20) = 2000 – 200e(-.044629)(20)

C(20) = 1918 critters