Question

the population of deer and wild boars on an island in the pacific ocean were recorded over a period of five years. the results are shown in the table. which statement best describes the results? time (in years) 0 1 2 3 4 5 deer 2200 2420 2640 2860 3080 3300 boars 3500 3850 4235 4659 5124 5637 options: the population of deer is growing exponentially. both populations are growing at an exponential rate. both populations are growing at a constant rate. the population of boars is growing exponentially.

Explanation:

To determine the growth pattern, we check the ratios of consecutive population values. For deer:

• \( \frac{2420}{2200} = 1.1 \)
• \( \frac{2640}{2420} = 1.1 \)
• \( \frac{2860}{2640} = 1.1 \)
• \( \frac{3080}{2860} = 1.1 \)
• \( \frac{3300}{3080} = 1.1 \) (constant ratio, exponential growth).

For boars:

• \( \frac{3850}{3500} = 1.1 \)
• \( \frac{4235}{3850} = 1.1 \)
• \( \frac{4659}{4235} = 1.1 \)
• \( \frac{5124}{4659} = 1.1 \)
• \( \frac{5637}{5124} = 1.1 \) (constant ratio, exponential growth).

So both populations grow exponentially.

Answer:

Both populations are growing at an exponential rate.