The problem
I need help with the following:
The population of Dog Patch was 80 in 2001 and 800 in 2015. Predict the population in 2020 using:
a) a linear growth model
b) an exponential growth model
Thank you for your help:)
Answer provided by our tutors
A linear growth model would be based on fitting two points to define a line. The points in the Dog Patch example are (80,2001) and (800,2015). As a formula you would obtain:
y-2001=((2015-2001)/(800-80)) * (x-80)
the plug in for y=2020:
x=1057.14
So the population linear would be approximately 1057.
An exponential growth model is relies on calculating a constant ratio for the known years and populations and then using that constant in order to calculate the new population model.
The constant comes from:
800 = 80k^(2015-2001)
k solves to approximately 1.179 and then replace 'k' with the constant, change '2015' to '2020' and calculate a new population (approximately 1821).