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.

Question

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.
Please make it simple.

Answer 1

To compare the growth rates of the deer population from 1–3 years and from 5–10 years, we can calculate the percentage growth for both intervals.

Growth from 1 to 3 years:

• Year 1 Deer Count: \( y(1) = 221 \)
• Year 3 Deer Count: \( y(3) = 373 \)

Change in Deer Population: \[ \text{Change} = y(3) - y(1) = 373 - 221 = 152 \]

Percentage Growth: \[ \text{Percentage Growth} = \left( \frac{\text{Change}}{\text{Initial Count}} \right) \times 100 = \left( \frac{152}{221} \right) \times 100 \approx 68.8% \]

Growth from 5 to 10 years:

• Year 5 Deer Count: \( y(5) = 631 \)
• Year 10 Deer Count: \( y(10) = 2344 \)

Change in Deer Population: \[ \text{Change} = y(10) - y(5) = 2344 - 631 = 1713 \]

Percentage Growth: \[ \text{Percentage Growth} = \left( \frac{\text{Change}}{\text{Initial Count}} \right) \times 100 = \left( \frac{1713}{631} \right) \times 100 \approx 271.1% \]

Summary:

• Growth from 1 to 3 years: approximately 68.8%
• Growth from 5 to 10 years: approximately 271.1%

Conclusion:

The growth rate of deer from 5 to 10 years (approximately 271.1%) is significantly higher than the growth rate from 1 to 3 years (approximately 68.8%).