Is the equation A=27500(0.75)t
a model of exponential growth or exponential decay, and what is the rate
of change per time period?
Responses
exponential growth and 25%
exponential growth and 25%
exponential decay and 25%
exponential decay and 25%
exponential decay and 75%
exponential decay and 75%
exponential growth and 75%
The equation A=27500(0.75)t is a model of exponential decay. The rate of change per time period is 25%.
The equation A=27500(0.75)t represents exponential decay and the rate of change per time period is 25%.
To determine whether the equation A = 27500(0.75)^t represents exponential growth or exponential decay, we need to analyze the value of the base, which is 0.75 in this case.
In exponential growth, the base value is greater than 1. This means that as the value of t (time period) increases, the value of A will also increase. However, in exponential decay, the base value is between 0 and 1. As t increases, the value of A will decrease.
In the given equation, the base value is 0.75, which is less than 1. Therefore, the equation represents exponential decay.
Now, let's determine the rate of change per time period. In this equation, the base (0.75) represents a decrease of 25% per time period. This means that each time period, the value of A will decrease by 25% of its previous value.
So, the correct answer is:
- The equation A = 27500(0.75)^t represents exponential decay.
- The rate of change per time period is 25%.