Question

The population of a small rural town in the year 2006 was 2,459. The population can be modeled by the function below, where f(x) is the number of residents and t is the number of years elapsed since 2006. Using the information given above, complete the following statements. The percent change is %. The percent change represents .

Answer 1

f(x)=2,459(0.92)^t

Using the information given above, complete the following statements. The percent change is %. The percent change represents .

f(x)=2,459(0.92)^t

Given equation is an exponential function and in the form of f(x) = a(1-r)^x

Where 'a' is the initial population

'r' is the decay rate

'x' is the time

f(x) = a(1-r)^x

Given function is f(x)=2,459(0.92)^t

1 - r = 0.92

r = 1 - 0.92

r = 0.08

r= 0.08 %

Percentage change = 0.08%

Percentage change represents the decay rate.

Answer 2

Answer:

8%, the rate at which the population is decreasing.

Step-by-step explanation:

Look at the equation f(x)=2,459(0.92)^t

0.92 represents the rate of change.

Because 0.92 is less than 1, it represents a decrease.

To calculate the rate of decay, subtract 0.92 from 1 (1 - 0.92 = 0.08)

To convert the rate of decay to percent, move the decimal to the right two spaces.

The answer is 8%, which represents the rate at which the population is decreasing.