# MATH

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4. The population of a small town is modelled by the function
p(t)= 20(4t+3)/2t+5
, where P(t) is the population, in thousands, and t is time, in years, since the start of 1990.

b) The town will need its own transit system if the population exceeds
50 000. Will the townâ€™s population ever exceed 50 000? Explain.

• MATH -

a little long division shows that
p(t) = 40 - 140/(2t+5)

As t increases, a smaller and smaller amount is subtracted from 40, so for all t>0, p(t) is increasing.

But, no matter how big t gets, p(t) < 40, so it indicates that the population will never exceed 50,000.

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