The growth of Mycobacterium tuberculosis bacteria can be modeled by the function N ( t ) = a e ^ { 0.166t }, where N is the number of cells after t hours and a is the number of cells when t = 0.

a.) At 1:00 P.M. there are 30 M. tuberculosis bacteria in a sample. Write a function that gives the number of bacteria after 1:00 P.M.

b.)Use a graphing calculator to graph the function in part(a).

C)Describe how to find the number of cells in the sample at 3:45 P.M

I NEED ALL 3 PARTS:))

C) The difference between 1 pm and 3:45 pm is equivalent to 2:45 minutes. In this case 45/60(45 mins/hour) is equal to 3/4 which really is .75. The 2 should be the hours so the answer is 2.75

Answer Link

eudora eudora · Answer 2 · 2022-01-28T19:26:00+01:00

a). Number of bacteria after 't' hours will be modeled by the function,

[tex]N(t)=30.e^{0.166t}[/tex]

b). Graph attached.

c). At 3:45 P.M., number of cells in the sample will be 47 (Approx.)

Given in the question,

Growth of the bacteria modeled by the function,

[tex]N(t)=ae^{0.166t}[/tex]

Here a = Number of cells at t = 0 Or at 1:00 pm.

t = Number of hours after 1 : 00 pm

a). If [tex]a=30[/tex] at 1 : 00 P.M.

Number of bacteria after 't' hours ⇒ [tex]N(t)=30.e^{0.166t}[/tex]

b). Find the graph of the function attached.

c). After 3:45 P.M.,

t = 2 hours 45 minutes

= [tex]2+\frac{45}{60}[/tex]

= 2.75 hours

Substitute these values in the given function,

[tex]N(2.75)=30.e^{0.166\times 2.75}[/tex]

[tex]N(2.75)=30.e^{0.4565}[/tex]

[tex]=47.356[/tex]

[tex]\approx47[/tex] cells

Learn more,

https://brainly.com/question/4332205