Question

Drag each tile to the correct box.

A scientist is studying the growth rates of three samples of bacteria in different conditions. The following three functions represent the number of bacteria in the three samples after x hours.


Order the samples by their average growth rate over the interval [1, 3], from least to greatest.

Answer 1

Answer: C < B < A

Explanation:

First, let's evaluate the growth rate of A from [1, 3]

`f(x) = 200\bigg((3)/(2)\bigg)^1`

= 300

coordinate is (1, 300)

`f(x) = 200\bigg((3)/(2)\bigg)^3`

= 675

coordinate is (3, 675)

Average growth rate (AGR) is:
`(675-300)/(3-1) = (375)/(2) = 187.5`

AGR (A) = 187.5

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Next, let's evaluate the growth rate of B from [1, 3]

The coordinates are already provided as (1, 120) and (3, 480)

Average growth rate (AGR) is:
`(480-120)/(3-1) = (360)/(2) = 180`

AGR (B) = 180

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Lastly, let's evaluate the growth rate of C from [1, 3]

f(x) = 600(1.2)ˣ

f(x) = 600(1.2)¹

= 720

coordinate is (1, 720)

f(x) = 600(1.2)³

= 1036.8

coordinate is (3, 1036.8)

Average growth rate (AGR) is:
`(1036.8-720)/(3-1) = (316.8)/(2) = 158.4`

AGR (C) = 158.4