At least one of the answers above is NOT correct. 1 of the questions remains una

Question

At least one of the answers above is NOT correct. 1 of the questions remains unanswered (1 point) Note: This problem has been slightly modified from the original appearing in Chapter 2 of Adler's Modeling the Dynamics of Life. Let P(t) = 4 × 105 + 4 × 103 t measure the number of individuals in a population. The mass pe individual is measured by W(t) 79-0.6t. Time is measured in years, mass in kilograms. The total mass of a population is the product of the number of individuals and the mass per individual Write a formula for the total mass as a function of time M(t) (400000+4000t)(79-0.6t) Compute the derivative of the total mass: M'(t) 76000-4800t For what value of t is the derivative 02t 15.83 What is the total mass when the derivative is zero? is the total mass increasing or decreasing after the time when the derivative is zero? decreasing Note: You can eam partial credit on this probiem Your score was recorded

Explanation / Answer

M(t) = P(t) *w(t)

M(t) = (400000+4000t)(79-0.6t)

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Find derivative using product rule as

M'(t) = 4000(79-0.6t) + (-0.6) (400000+4000t)

=76000 -4800t

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when M'(t) = 0

76000 -4800t = 0

4800t =76000

t =76000 /4800

t=15.83

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when t =76000 /4800 =15.83 find M(t) as

M(t) =(400000+4000*76000 /4800)(79-0.6*76000 /4800)

=32201666.67

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Decreasing

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