document.write( "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 \n" ); document.write( "

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\n" ); document.write( " $\"p%28t%29=200%280.8%29%5E%28t%2F10%29\"$

\n" ); document.write( "That is a decaying exponential function. Every 10 years, the population gets multiplied by 0.8 or 80% -- i.e., decreases by 20%.

\n" ); document.write( "The range of any decaying exponential function for positive t is from 0 to the starting value.

\n" ); document.write( "Domain: [0,infinity)
\n" ); document.write( "Range: [200,0)

\n" ); document.write( "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].

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