Question

The growth of Mycobacterium tuberculosis bacteria can be modeled by the function N(t) = ae0.166t , where N is the number of cells after t hours and a is the number of cells when t = 0.

(1) At 1:00PM, there are 42 M. tuberculosis bacteria in a sample. Write a function that gives the number of bacteria after 1:00PM.
(2) What is the rate of growth in this model?
(3) Calculate the number of cells in the sample at 3:45PM

Answer 1

To write a function that gives the number of bacteria after 1:00PM, substitute a = 42 and t = 1 into the growth function. The rate of growth in this model is 0.166. The number of cells in the sample at 3:45PM can be calculated by substituting t = 3.75 into the growth function.

Step-by-step explanation:

To write a function that gives the number of bacteria after 1:00PM, we need to substitute the given information into the growth function. In this case, a = 42 (the number of cells at t = 0) and t = 1 (since 1:00PM is one hour after t = 0). So the function becomes N(t) = 42e^(0.166*1) = 42e^0.166.

The rate of growth in this model is given by the coefficient 0.166. The rate indicates how fast the number of cells increases for each unit of time (in this case, t = 1 hour).

To calculate the number of cells in the sample at 3:45PM, we substitute t = 3.75 (since 3:45PM is 3 hours and 45 minutes after t = 0) into the growth function. So the function becomes N(3.75) = 42e^(0.166*3.75).