A town has a population of 9000 and grows at every year. What will be the population after 9 years, to
the nearest whole number?

Question

A town has a population of 9000 and grows at $$ 3 \% $$ every year. What will be the population after 9 years, to the nearest whole number?

UpStudy AI · Accepted Answer

We start with the formula for compound growth:

$$
P = P_0 (1 + r)^t
$$

where:
- $$ P_0 = 9000 $$ is the initial population,
- $$ r = 0.03 $$ is the annual growth rate,
- $$ t = 9 $$ is the number of years.

Substituting the given values:

$$
P = 9000 (1 + 0.03)^9 = 9000 (1.03)^9
$$

Next, we calculate $$(1.03)^9$$. This value is approximately:

$$
(1.03)^9 \approx 1.30478
$$

Now, multiplying by the initial population:

$$
P \approx 9000 \times 1.30478 \approx 11743.02
$$

Rounding to the nearest whole number, the population after 9 years will be:

$$
P \approx 11743
$$
After 9 years, the population will be approximately 11,743.

Solución de inteligencia artificial de Upstudy