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.

Answer 1

To compare the growth rate of deer from 1–3 years with the growth rate from 5–10 years, we can calculate the growth in deer population for each specified period and then find the percentage increase.

Growth Rate from 1 to 3 Years

1. Number of deer at year 1: \( y(1) = 221 \)
2. Number of deer at year 3: \( y(3) = 373 \)

Change in the number of deer: \[ \Delta y = y(3) - y(1) = 373 - 221 = 152 \]

Percentage increase from year 1 to year 3: \[ \text{Percentage Increase} = \left( \frac{\Delta y}{y(1)} \right) \times 100 = \left( \frac{152}{221} \right) \times 100 \approx 68.8% \]

Growth Rate from 5 to 10 Years

1. Number of deer at year 5: \( y(5) = 631 \)
2. Number of deer at year 10: \( y(10) = 2344 \)

Change in the number of deer: \[ \Delta y = y(10) - y(5) = 2344 - 631 = 1713 \]

Percentage increase from year 5 to year 10: \[ \text{Percentage Increase} = \left( \frac{\Delta y}{y(5)} \right) \times 100 = \left( \frac{1713}{631} \right) \times 100 \approx 271.6% \]

Comparison of Growth Rates

• Growth from Year 1 to 3: approximately 68.8%
• Growth from Year 5 to 10: approximately 271.6%

Conclusion

The growth rate of the deer population from Year 5 to Year 10 (approximately 271.6%) is significantly higher than the growth rate from Year 1 to Year 3 (approximately 68.8%). Thus, the deer population grows much more rapidly in the later years compared to the early years.