High School

An ant population (in thousands) grows each month according to the model [tex]A(m) = 4.7 \times 1.5^m[/tex]. When will the population reach 38.2 thousand?

Answer :

The ant population will reach 38.2 thousand in about 3.25 years, assuming a growth rate of 5% per year.

To answer this question, we need to know the growth rate of the ant population. Let's say the growth rate is 5% per year. This means that each year, the population will increase by 5% of its current size. To calculate the population size after a certain number of years, we can use the formula:

P = P0 * (1 + r)^t

where P is the population size after t years, P0 is the initial population size, r is the growth rate as a decimal, and t is the number of years.

Assuming the initial population size is 30 thousand, we can plug in the values to find when the population will reach 38.2 thousand:

38.2 = 30 * (1 + 0.05)^t

Solving for t, we get t = 3.25 years. However, it's important to note that the actual growth rate may be different, so this calculation is just an estimate.

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