The number of jobs grows exponentially over time based on the existing number of jobs. Given there were 15 million jobs initially and 15.1 million jobs 3 months later, the model estimates there will be 15.8 million jobs in two years. A population of critters increases directly proportional to the difference between its maximum size and current size. Given the population was initially 1800 and 1750 after 5 years, the model estimates the population will be 1918 critters after 20 years.

1. Diff EQ Quest

2. Exponential Growth
 In 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?

3. Exponential Growth
 f(t) = number of people with jobs at time t months
 f’(t) = k f(t) for some constant t
 Given f(0) = 15, then f(t) = 15ekt
 Given f(3) = 15.1, then k = 0.002215
 At 24 months, f(24) = 15.8 million jobs

4. Population Problem
 A 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)

5. Solution
 C(t) = 2000 – 200e-kt
 k = -.044629
 C(20) = 2000 – 200e(-.044629)(20)
 C(20) = 1918 critters