Question

test yourself! practice tool
the population in a small town is modeled by the function $p(t) = 4000 \cdot (1.01)^t$ where $p$ is the population and $t$ is the number of years since 1990.
complete the statements.
based on the function $p(t) = 4000$ is the population of the town in 1990. the population of the town is each year.
options for the second blank: increasing by 1%, decreasing by 99%, increasing by 4000%

Explanation:

Step1: Identify growth function form

The given function is an exponential growth model: $P(t) = P_0(1+r)^t$, where $P_0$ is the initial population, $r$ is the annual growth rate, and $t$ is time.

Step2: Match to given function

Compare $P(t)=4000\cdot(1.01)^t$ to the model: $1+r=1.01$, so solve for $r$.
$r = 1.01 - 1 = 0.01$, which is $1\%$.

Answer:

increasing by 1%