Question

A town has a population of 4155 people at time t=0.

The population increases by 5% per year.
Enter a formula for the population, P, of the town as a function of year t.
P(t) =
a. P(t)=4155×(1+0.05) t
b.P(t)=4155×e 0.05t
c. P(t)=4155+0.05t
d. P(t)=4155×(21/20) t

Answer 1

The applicable formula for the population of the town as a function of time with a 5% yearly increase is P(t) = 4155 × (1 + 0.05)^t.

Step-by-step explanation:

The question involves finding a formula for the population growth of a town as a function of time, given a 5% annual increase. To model this, we use an exponential growth equation. The correct formula would take the initial population and apply the exponential growth factor raised to the power of the number of years, t.

The population at time t=0 is 4155. With an increased rate of 5% per year, the formula would be P(t) = 4155 × (1 + 0.05)^t. Therefore, the correct answer is a. P(t) = 4155 × (1 + 0.05)^t.