Question

There are 170 deer on a reservation. The deer population is increasing at a rate of 30% each year. The table shows the number of deer, y, after x years.

Use the table to answer the question.

Years (x) 0 1 3 5 10
Deer (y) 170 221 373 631 2344
How does the growth rate of deer from 1–3 years compare to the growth rate of deer from 5– 10 years? Show your work.

(2 points)

Answer 1

Compute the annual growth rate r from x1 to x2 by r = (y2/y1)^(1/(x2−x1)) − 1.

1–3 years:
y1 = 221, y2 = 373, years = 2
r = (373/221)^(1/2) − 1 = 1.68733^(1/2) − 1 ≈ 1.2997 − 1 = 0.2997 ≈ 29.97% ≈ 30%

5–10 years:
y1 = 631, y2 = 2344, years = 5
r = (2344/631)^(1/5) − 1 = 3.7149^(1/5) − 1 ≈ 1.2996 − 1 = 0.2996 ≈ 29.96% ≈ 30%

Conclusion: The growth rates are the same — about 30% per year.