Question

A small town's population is declining at a rate of 4% per year. The initial population of the town was 13,600.

1. Write an equation to model the situation where p represents the town's population and t represents years.

2. Use your equation to predict the population of the town in 20 years.​

Answer 1

1.

The equation to model the situation can be written as:

`\boxed{\bold{P = P_o*(1-r\%)^t}}`

Where:

P represents the town's population

`P_o` represents the current population

r represents the rate percentage per year

t represents the number of years

substituting value,

`\boxed{\bold{P= 13,600 * (1 - 0.04)^t}}` is the required equation.

2.

We substitute t = 20 into the equation and solve for p, to predict the population of the town in 20 years.

`\bold{P= 13,600 * (1 - 0.04)^(20)=6,011.23}`

Therefore, the predicted population of the town in 20 years is approximately 6,011 people.