SOLUTION: A biologist estimates there are 200 animals of a certain species in a particular region. He expects the function p(t)=200(0.8)^t/10 to model the future population of the species, w

Algebra ->  Trigonometry-basics -> SOLUTION: A biologist estimates there are 200 animals of a certain species in a particular region. He expects the function p(t)=200(0.8)^t/10 to model the future population of the species, w      Log On


   

Question 1181882: A biologist estimates there are 200 animals of a certain species in a particular region. He expects the function p(t)=200(0.8)^t/10 to model the future population of the species, where p(t) is the population t years after the initial count. The range of the model function is
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


p%28t%29=200%280.8%29%5E%28t%2F10%29

That is a decaying exponential function. Every 10 years, the population gets multiplied by 0.8 or 80% -- i.e., decreases by 20%.

The range of any decaying exponential function for positive t is from 0 to the starting value.

Domain: [0,infinity)
Range: [200,0)

Note mathematically the function value never reaches 0. However, a population of animals is a whole number; so if the trend of the decaying exponential continues, the population will eventually be 0 -- making the range [200,0].