Which scenario could best represent the equation f(t)=400⋅1.15t

Question

(1 point)
Responses

A population of mice has a monthly growth rate of 15%.
A population of mice has a monthly growth rate of 15%.

A population of birds starts at 400 and has an annual growth rate of 15%.
A population of birds starts at 400 and has an annual growth rate of 15%.

A bee hive that starts at a population of 400 and decays 15% annually.
A bee hive that starts at a population of 400 and decays 15% annually.

A friend loans you $400 and charges you 1.15% interest on it each month.

Answer 1

The equation \( f(t) = 400 \cdot 1.15^t \) represents a scenario where a quantity starts at 400 and increases by a factor of 1.15 for each time period \( t \). The factor 1.15 indicates that the growth rate is 15%.

Given the options provided, the scenario that best represents this equation is:

A population of birds starts at 400 and has an annual growth rate of 15%.

This is because the population starts at 400 and grows by 15% each period (assuming \( t \) is measured in years). The other options do not align correctly with the growth indicated by the equation.