Calculus for Business

Question

A major corporation is building a large complex of homes, offices, stores schools, and churches. As a result of this development, the planners have estimated that the town’s population (in thousands) t years from now will be given by the formula

P(t) = 17t^2 +17t + 20/ 2t^2 + 5t +40

a. What is the current population of the town? Use appropriate units and round your answer to the nearest whole number.

b. What will be the population of the town in the long run? Use appropriate units and round your answer to the nearest whole number.

Answer 1

a. P(0) = 20/40 = 0.5 thousand people.

b. lim t →∞P(t) = 17/2 = 8.5 thousand people

Answer 2

For

to find the "current" population, you would plug in t = 0 which give

p(0) = 20/40 = 0.5 thousand people or 500 people.

Ultimately, as t gets larger and larger, the population approaches the division of the leading coefficients (17 and 2) so 17/2 = 8.5 thousand people = 8,500 people.

Try it for t = 10 and larger:

P(10) = 6.5

P(100) = 8.4

P(1000) = 8.49)

P(10,000) = 8.499

P(100,000) = 8.4999

P(1,000,000) = 8.49999