Question

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 #3

Option #2

Option #4

Option #1

Answer 1

Option #2

Reason: f(0)=3 and f(1)=3(1.25)=3.75 ≈4, f(5)=3(1.25)^5 ≈9.16 ≈9, so the dotted curve (Option 2) matches the exponential growth.