Question

The bluestripe snapper is an invasive species in the hawaiian islands. their population grows exponentially with a growth rate of 24.3 % per year. by what factor will the bluestripe snapper population currently in the hawaiian islands grow by over the next 7 years? use two decimal accuracy.

Answer 1

The bluestripe snapper population in the Hawaiian Islands is expected to grow by a factor of about 2.47 over the next 7 years based on an annual growth rate of 24.3%.

Step-by-step explanation:

The bluestripe snapper population in the Hawaiian Islands:

The bluestripe snapper population in the Hawaiian Islands, with a growth rate of 24.3% per year, will grow by a factor of approximately 2.47 over the next 7 years. To calculate this growth, we apply the formula for exponential growth P(t) = P(0) * e^(rt), where P(t) is the future population, P(0) is the current population, r is the growth rate, and t is time. Substituting the given growth rate of 24.3% (or 0.243) and 7 years into the formula, we get:

Growth Factor = (1 + 0.243)^7 ≈ 2.086

Therefore, the bluestripe snapper population will multiply by a factor of approximately 2.086 over the next 7 years in the Hawaiian Islands. Here, we can disregard P(0) as we're interested in the growth factor, so we simplify to e^(rt). Plugging in the growth rate r = 0.243 and time t = 7 years, we have e^(7*0.243), which calculates to a growth factor of approximately 2.47 when rounded to two decimal places.