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At the beginning of an experiment, the number of bacteria in a colony was counted at time t = 0. The number of bacteria in the colony t minutes after the initial count is modeled by the function f(t) = 4(2)t. Which value and unit represent the average rate of change in the number of bacteria for the first 5 minutes of the experiment?

I. 20
II. 24.8
III. minutes per bacteria
IV. bacteria per minute
A) I only
B) I & III
C) II only
D) II & IV

Respuesta :

Option D: II and IV represents the average rate of change in the number of bacteria for the first 5 minutes in the experiment

Explanation:

Given that the number of bacteria in the colony t minutes after the initial count is modeled by the function [tex]f(t)=4(2)^t[/tex]

We need to determine the value and unit that represent the average rate of change in the number of bacteria for the first 5 minutes of the experiment.

The rate of change of bacteria can be determined using the slope formula.

The number of bacteria at time [tex]t=0[/tex] is given by

[tex]f(0)=4(2)^0[/tex]

[tex]f(0)=4[/tex]

The number of bacteria at time [tex]t=5[/tex] is given by

[tex]f(5)=4(2)^5[/tex]

[tex]f(5)=4(32)[/tex]

[tex]f(5)=128[/tex]

The average rate of change is given by

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting the coordinates [tex](0,4)[/tex] and [tex](5,128)[/tex] , we have,

[tex]m=\frac{128-4}{5-0}[/tex]

[tex]m=\frac{124}{5}[/tex]

[tex]m=24.8[/tex]

Thus the average rate of change is 24.8 bacteria per minute.

Therefore, Option D is the correct answer.

ashishdwivedilVT

The average rate of change in the number of bacteria for the first 5 minutes of the experiment is 24.8 bacteria per minute.

Given function is,

[tex]f(t) = 4(2^t)[/tex]

What is the average rate of change?

It is a measure of how much the function changed per unit, on average, over an interval.

[tex]f(0) = 4(2^0) = 4\\f(5) = 4(2^5) = 128[/tex]

The average rate of change

[tex]=\frac{f(5)-f(0)}{5-0}[/tex]

[tex]=\frac{128-4}{5} \\\\=\frac{124}{5\\}[/tex]

[tex]=24.8[/tex]

Therefore, the average rate of change in the number of bacteria for the first 5 minutes of the experiment is 24.8 bacteria per minute.

To get more about the average rate of change visit:

https://brainly.com/question/8728504

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