Question

A model predicts that the population of a certain town was 10,000 in 2001. The model also
predicts that each year for the next 5 years, the population p increased by 8% of the previous
year's population. Which equation best represents this model, where X is the number of years after
2001, for X < 5?

Answer 1

Answer:

The equation that best represents this model is $P(x) = 10000(1.08)^x$

Step-by-step explanation:

Exponential equation for population growth:

The exponential equation for population growth, after x years, is given by:

$P(x) = P(0)(1+r)^x$

In which P(0) is the initial population and r is the growth rate.

A model predicts that the population of a certain town was 10,000 in 2001.

This means that $P(0) = 10000$

8% yearly increase.

This means that $r = 0.08$. So

$P(x) = P(0)(1+r)^x$

$P(x) = 10000(1+0.08)^x$

$P(x) = 10000(1.08)^x$

The equation that best represents this model is $P(x) = 10000(1.08)^x$