Question

The weight of a population of yeast is given by a differentiable function, W, where W(t) is measured in grams and t is measured in hours. The weight of the yeast population increases with respect to t at a rate that is directly proportional to the weight. At time t=10 hours, the weight of the yeast is 200 grams and is increasing at the rate of 5 grams per hour. Which of the following is a differential equation that models this situation?

Answer 1

Answer: dW/dt=1/40 W

Explanation:dW/dt=kW, k is a constant

dW/dt=5 when W=200

5=200k

k=5/200

=1/40

Answer 2

The differential equation that models this situation is dW/dt=1/40 W.

Differential equation

Given:

Weight=200 grams

Rate=5 grams per hour

Using this formula

dW/dt=kW where k is constant

dW/dt=5

W=200

Hence:

5=200k

k=5/200 or 1/40

Inconclusion the differential equation that models this situation is dW/dt=1/40 W.

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