Question

Use the image to answer the question.

Four curves are graphed on a coordinate plane. The x-axis is labeled Time in Years and ranges from 0 to 10 in increments of 1. The y-axis is labeled Population and ranges from 0 to 200 in increments of 25.
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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 72 right parenthesis, left parenthesis 2.2 comma 150 right parenthesis, and left parenthesis 3 comma 200 right parenthesis. The second curve is dotted and is labeled Option 2. The second curve passes through approximate coordinates left parenthesis 0 comma 72 right parenthesis, left parenthesis 6 comma 87.5 right parenthesis, and left parenthesis 8 comma 100 right parenthesis. The third curve is dot-dashed and is labeled Option 3. The third curve passes through approximate coordinates left parenthesis 0 comma 72 right parenthesis, left parenthesis 4 comm a 67.5 right parenthesis, and left parenthesis 8 comma 55 right parenthesis. The fourth curve is dashed and is labeled Option 4. The fourth curve passes through coordinates left parenthesis 0 comma 72 right parenthesis, left parenthesis 2 comma 25 right parenthesis, and left parenthesis 10 comma 0 right parenthesis.

A herd of zebras is declining at a rate of 4% each year. The herd currently has 72 zebras. Of the four functions graphed in the image, which correctly models the population decline?

(1 point)
The graph that correctly models the population decline is Option #
.

Answer 1

The answer is option 4

Answer 2

Option 3

Reason: A 4% annual decline is exponential (P(t)=72(0.96)^t), a gradual decrease. Of the four graphs only Option 3 shows a modest exponential-like decline (the others increase or drop too fast/linearly).