A biologist studying a population of alligators in a State Park determines that the population can be modelled by the
formula ff(tt) = 120,000(1.015)tt
, where ff(tt) represents the population after t years. An intern studying with the
biologist makes this claim: “Based on the formula, after 1 year the population will have increased by 1800. Since 1800
divided by 12 is 150, we can used the fact that the population increases by 150 Alligators per month to predict the future
population of alligators in the park.”
Explain why the intern’s claim is not valid.
Modify the initial given formula such that it represents the predicted population after m months, and use the formula to
predict the population after 50 months.
The intern's claim is not valid because they have made an incorrect assumption about the rate at which the population increases. The intern assumes that since the increase after 1 year is 1800, the population must be increasing by 150 alligators per month. However, this is an incorrect assumption.
To determine the increase in population per month, we need to find the monthly growth rate. The given formula represents the population as a function of time in years, so we need to convert the time to months. Since there are 12 months in a year, we can divide t by 12 to convert it to months.
So, the modified formula to represent the predicted population after m months would be:
f(m) = 120,000(1.015)^(m/12)
Now, to predict the population after 50 months, we can substitute m = 50 into the formula:
f(50) = 120,000(1.015)^(50/12)
Calculating this value will give us the predicted population after 50 months.