Some time in the future a human colony is started on Mars Th

Some time in the future a human colony is started on Mars. The colony begins with 40000 people and grows exponentially to 120000 in 200 years. Give a formula for the size of the human population on Mars as a function of t = time (in years) since the founding of the original colony 40000e^(.00549t) Assuming the population continues to grow exponentially, how long will it take to reach a size of 240000? 326.367 years What is the rate of change of the size of the population (measured in people per year) 150 years after the founding of the original colony? 5000 people/year

Solution

after 150 years

rate of change of population would be (by differentiating 4000e^(0.00549t) w.r.t t and putting t = 150)

i.e.

4000 * 0.00549 e^(0.00549 * 150) = 50.03

Concept is the rate of growth is determined by the derivative of growth function