Question

If an exponential function has a growth factor of 0.9, what is the percent rate of change?

A) -10%
B) -90%
C) 10%
D) 90%

Answer 1

The percent rate of change for an exponential function with a growth factor of 0.9 is -10%, reflecting a 10% decrease per time period.

Step-by-step explanation:

If an exponential function has a growth factor of 0.9, the percent rate of change can be calculated by subtracting this growth factor from 1 and then multiplying by 100 to convert to a percentage. The growth factor represents the ratio of the new amount to the original amount after each time period. Since the growth factor here is less than 1, this indicates a decrease rather than an increase.

The percent rate of change is calculated as follows:

1. Subtract the growth factor from 1: 1 - 0.9 = 0.1.
2. Multiply by 100 to convert to a percentage: 0.1 × 100 = 10%.

However, because the growth factor is less than 1, this actually represents a reduction in value. Therefore, the percent rate of change is -10%, which represents a 10% decrease for each period of time in question.

So, the correct answer to the question "If an exponential function has a growth factor of 0.9, what is the percent rate of change?" is A) -10%.