Question

Use the image to answer the question.

Four curves are graphed on a coordinate plane. The x-axis is labeled Time in Days and ranges from 0 to 6 in increments of 1. The y-axis is labeled Population and ranges from 0 to 25 in increments of 5.
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The first curve is solid and is labeled Option 1. The first curve passes through approximate coordinates left parenthesis 0 comma 3 right parenthesis, left parenthesis 3 comma 0 right parenthesis, and left parenthesis 6 comma 0 right parenthesis. The second curve is dotted and is labeled Option 2. The second curve passes through approximate coordinates left parenthesis 0 comma 3 right parenthesis, left parenthesis 1 comma 4 right parenthesis, and left parenthesis 5 comma 9 right parenthesis. The third curve is dot-dashed and is labeled Option 3. The third curve passes through approximate coordinates left parenthesis 0 comma 3 right parenthesis, left parenthesis 1 comma 2 right parenthesis, and left parenthesis 5 comma 1 right parenthesis. The fourth curve is dashed and is labeled Option 4. The fourth curve passes through approximate coordinates left parenthesis 0 comma 3 right parenthesis, left parenthesis 0.5 comma 15 right parenthesis, and left parenthesis 0.75 comma 25 right parenthesis.

The function f(x)=3(1.25)x
represents the population growth of a swarm of fruit flies. Create a graph modeling the equation, and determine which graph models the situation accurately.

(1 point)

Option #2

Option #3

Option #1

Option #4

Answer 1

Option #2

Reason: f(1) = 3(1.25) = 3.75 ≈ 4 and f(5) ≈ 9.16, so the slowly increasing curve that passes near (1,4) and (5,9) (Option 2) matches 3(1.25)^x.