Question

The number of cells in a laboratory culture increases rapidly initially but levels off eventually. The population of cells is modeled by the logistics function P(t) = a / (1 + be^-t) Where a & b are positive real numbers and t is measured in hours. At t=0 hours, the population is 25 cells and is increasing at a rate of 15 cells/hour. a) Find the values of "a" and "b." *Hint: You will need to set up and solve a system of equations based on the given information. b) According to the model, what happens to the population of cells in the long term (called the "carrying capacity")? Be sure to show work justifying your answer.

          The number of cells in a laboratory culture increases rapidly initially but levels off eventually. The population of cells is modeled by the logistics function
P(t) = a / (1 + be^-t)
Where a & b are positive real numbers and t is measured in hours. At t=0 hours, the population is 25 cells and is increasing at a rate of 15 cells/hour.
a) Find the values of "a" and "b."
*Hint: You will need to set up and solve a system of equations based on the given information.
b) According to the model, what happens to the population of cells in the long term (called the "carrying capacity")? Be sure to show work justifying your answer.

The number of cells in a laboratory culture increases rapidly initially but levels off eventually. The population of cells is modeled by the logistics function
P(t) = a / (1 + be^-t)
Where a b are positive real numbers and t is measured in hours. At t=0 hours, the population is 25 cells and is increasing at a rate of 15 cells/hour.
a) Find the values of "a" and "b."
*Hint: You will need to set up and solve a system of equations based on the given information.
b) According to the model, what happens to the population of cells in the long term (called the "carrying capacity")? Be sure to show work justifying your answer.

Added by Ashley L.

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