Question

The Bluestripe Snapper is an invasive species in the Hawaiian Islands. Their population grows exponentially with a growth rate of 24.8% per year. What is the expected size of a Hawaiian population of 244 Bluestripe Snapper that grows exponentially for 58 months?

Answer 1

Using the exponential growth formula with an initial population of 244 and a growth rate of 24.8% per year, the expected population size of Bluestripe Snapper after 58 months is approximately 817.

Step-by-step explanation:

To calculate the expected size of a Hawaiian population of Bluestripe Snapper after 58 months with a yearly exponential growth rate of 24.8%, we use the exponential growth formula: P(t) = P0 × e(rt), where P(t) is the future population size, P0 is the initial population size, e is the base of the natural logarithm (approximately 2.71828), r is the growth rate as a decimal, and t is the time in years. Since we have a monthly growth period, we convert 58 months into years by dividing by 12.

Step-by-step calculation:

• Initial population P0 = 244
• Growth rate r = 0.248 per year
• Time t = 58 months = 58/12 years
• P(58/12) = 244 × e(0.248 × 58/12)

Using a calculator, we find:

• P(58/12) ≈ 244 × e(1.208)
• P(58/12) ≈ 244 × 3.3472
• P(58/12) ≈ 817.296

The expected population size after 58 months is approximately 817 Bluestripe Snapper.