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

Step-by-step explanation:

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

$f(x) = 200\bigg(\dfrac{3}{2}\bigg)^1$

    = 300

coordinate is (1, 300)

$f(x) = 200\bigg(\dfrac{3}{2}\bigg)^3$

    = 675

coordinate is (3, 675)

Average growth rate (AGR) is: $\dfrac{675-300}{3-1} = \dfrac{375}{2} = 187.5$

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: $\dfrac{480-120}{3-1} = \dfrac{360}{2} = 180$

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: $\dfrac{1036.8-720}{3-1} = \dfrac{316.8}{2} = 158.4$

AGR (C) = 158.4