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The number of snowplows needed by a town is given by s(p)=0.5p−0.01p^2. snowplows where p is...

The number of snowplows needed by a town is given by

s(p)=0.5p−0.01p^2. snowplows where p is the population (in thousands).

The projected population of the town t years from now is p(t)=150(1+12e^−0.02t)^-1 thousand people.

(a) Write the model for the rate-of-change of the number of snowplows needed t years from now.

(b) What will be the rate-of-change of the number of snowplows needed five years from now?

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