Question

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?

Answer 1

0.39million cells/hour.

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.