At time t = 0, a bacterial culture weighs 4 grams. Three hours later, the culture weighs 5 grams. The maximum weight of the culture is 40 grams.

Question

(c) When will the culture's weight reach 32 grams? (Round your answer to two decimal places.)

(e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.)

Answer 1

Hi Jay P.,

You always assume the growth is exponential y(t) = y(0)exp(k*t) . So put your data in and solve for k (the time constant), and then use it to solve the other stated conditions. The culture is increasing in mass most rapidly immediately prior to "hitting the wall"; you don't have an equation supplied to provide a "soft landing" to the culture's growth which would indicate otherwise, and you don't have information which you could bootstrap into attempting a modeled solution for that -- are nutrients being depleted; are metabolic products accumulating, and so on.

--Cheers, --Mr. d.