Suppose that dP/dt = 0.13P (t) represents a mathematical model for the growth of a certain cell culture, where P (t) is the size of the culture (measured in millions of cells) at time t > 0 (measured in hours). How fast is the culture growing at the time t when the size of the culture reaches 3 million cells?

Question

Mathematics

Baylee Payne

31 August, 08:11

Suppose that dP/dt = 0.13P (t) represents a mathematical model for the growth of a certain cell culture, where P (t) is the size of the culture (measured in millions of cells) at time t > 0 (measured in hours). How fast is the culture growing at the time t when the size of the culture reaches 3 million cells?

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Daniels · Answer 1

0.39million cells/hour.

Step-by-step explanation:

dP/dt = 0.13P (t)

P (t) is the size of the culture

How fast is the culture is the question asked i. e the rate of P

dP/dt=?

Given that

P (t) = 3milions cells at time t

Then,

dP/dt = 0.13P (t)

dP/dt = 0.13 * 3milion cells

dP/dt = 0.39million cells/hour.