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

Years (x) 0, 1, 3, 5, 10
Deers (y) 170, 221, 373, 621, 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 simple

Answer 1

To compare the growth rates of the deer population from years 1–3 and 5–10, we first need to determine the number of deer at each of these points and then calculate the growth rate.

Step 1: Calculate the growth from year 1 to year 3

• At year 1: \( y = 221 \)
• At year 3: \( y = 373 \)

Growth from year 1 to year 3: \[ \text{Growth} = \text{Deers at year 3} - \text{Deers at year 1} = 373 - 221 = 152 \]

Calculate the growth rate: \[ \text{Growth Rate} = \frac{\text{Growth}}{\text{Deers at year 1}} \times 100 = \frac{152}{221} \times 100 \approx 68.8% \]

Step 2: Calculate the growth from year 5 to year 10

• At year 5: \( y = 621 \)
• At year 10: \( y = 2344 \)

Growth from year 5 to year 10: \[ \text{Growth} = \text{Deers at year 10} - \text{Deers at year 5} = 2344 - 621 = 1723 \]

Calculate the growth rate: \[ \text{Growth Rate} = \frac{\text{Growth}}{\text{Deers at year 5}} \times 100 = \frac{1723}{621} \times 100 \approx 277.6% \]

Conclusion

• Growth rate from year 1 to year 3: approximately 68.8%
• Growth rate from year 5 to year 10: approximately 277.6%

Comparison: The growth rate of deer from years 5 to 10 (approximately 277.6%) is significantly higher than the growth rate from years 1 to 3 (approximately 68.8%).