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

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) (Show Source): You can put this solution on YOUR website!

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].

RELATED QUESTIONS
A biologist estimates there are 500 animals of a certain species in a particular region.... (answered by math_tutor2020)

Preliminary remark. This is an interesting question showing how, based on a mathematical... (answered by josgarithmetic,ikleyn,math_tutor2020)

A biologist estimates that 70% of deer in the region carry a certain type of tick. For a (answered by stanbon)

A conservation organization releases 100 animals of an endangered species into a game... (answered by ankor@dixie-net.com)

A conservation organization releases 100 animals of an endangered species into a game... (answered by stanbon)

The graph of a function P(t) represent the size of a growing deer population over time.... (answered by ikleyn)

the length of time, t (in days), for 25 animals of a particular variety to grow to a... (answered by reviewermath)

A biologist introduces 200 ladybugs into a crop field. The population P of ladybugs is... (answered by Fombitz)

A biologist estimates that 40% of the deer in a region carry a certain type of tick. For... (answered by rothauserc)