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.

Question

Abbie Bowen

Mathematics

13 November, 18:00

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.

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Answers (2)

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Tiara · Answer 1

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.

Jacqueline Casey · Answer 2

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.