Suppose that dP/dt = 0.19P (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 2 million cells?

Question

Giovani Stanton

Mathematics

13 April, 04:24

Suppose that dP/dt = 0.19P (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 2 million cells?

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Porter Case · Answer 1

Answer: 380000 cells/hour

Step-by-step explanation:

Given that dP/dt = 0.19P (t)

where

P (t) is the size of the culture (measured in millions of cells) at time t > 0 (measured in hours).

The formula above represents a mathematical model for the growth of a certain cell culture. In essence, it represents the time rate of the growth of the cell culture, that is how fast the cell culture is growing.

Therefore, when P = 2 million cells:

dP/dt = 0.19 * 2000000 = 380000 cells/hour

Hence, the cell culture is growing at 380000 cells per hour.