Rate of Growth (Jump to: Lecture | Video )

In 1950, a city had a population of 20,000. Every year after that, the population increased by 2%. What was the population in 1990?

We can solve this problem using the following equation:

Figure 1.

y = final amount

a = initial amount

r = rate of growth

t = time

We can arrange our knowns to solve for the unknown:

Figure 2.

The population was 44,200 in 1990.

Below, we have two cities and their associated growth equations:

Figure 3.

When will City B’s population overtake City A’s?

We set City B to be greater than City A to determine the exact moment its population becomes greater.

Figure 4.

City B's population will overtake City A's after 9.28 years.