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 decay and 25%
exponential decay and 25%
exponential growth and 75%
exponential growth and 75%
exponential decay and 75%
exponential decay and 75%
exponential growth and 25%
The equation A=27500(0.75)t is a model of exponential decay, and the rate of change per time period is 25%.
To determine if the equation A=27500(0.75)t represents exponential growth or decay, we need to look at the value of the base, which is 0.75 in this case.
In exponential growth, the base is greater than 1, and each term in the equation is multiplied by a number greater than 1 as t increases. On the other hand, in exponential decay, the base is between 0 and 1, and each term in the equation is multiplied by a number less than 1 as t increases.
In this equation, the base is 0.75, which is less than 1. Therefore, the equation A=27500(0.75)t represents exponential decay.
Now, to find the rate of change per time period, we can look at the value of the base multiplied by 100%. In this case, the base is 0.75, so the rate of change per time period is 0.75 * 100% = 75%.
Therefore, the correct answer is: exponential decay and 75%.