The total world population is forecast to be P(t) = 0.00081t^3 - 0.0711t^2 + 0.9

Question

The total world population is forecast to be P(t) = 0.00081t^3 - 0.0711t^2 + 0.98t + 6.04 (0 less than equal to t less than equal to 10) in year t, where t is measured in decades, with t r 0 corresponding to 2000 and P(t) is measured in billions. (a) World population is forecast to peak in what year? Hint Use the quadratic formula. (Remember that t is in decades and not in years. Round your answer down to the nearest year.) (b) At what number will the population peak? (Be sure to use the value of t found in part (a). Round your answer to two decimal places.) billion

Explanation / Answer

For the first part differentiate with respect to t. You will get a quadratic equation. set it to zero and find its roots. the positive value will be the answer.

for part b, put the value obtained above in the cubic equation and get the answer

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