Final answer:
The percent rate of change of the function y=250(0.81)^x for each unit of x is found to be 19% by subtracting the base of the exponent from 1 and multiplying by 100.
Step-by-step explanation:
The problem at hand is to find the percent rate of change of the function y=250(0.81)^x for each unit change in x. This type of function is an exponential decay function where 0.81 is the base of the exponent and represents the percent change per unit increase in x. To find the percent rate of change, we calculate the rate at which y decreases as x increases by 1. Here's the process:
- Identify the base of the exponential. In our case, it's 0.81.
- Subtract the base from 1 to get the percent change per unit. So, 1 - 0.81 = 0.19.
- To express this as a percentage, multiply by 100. Therefore, 0.19 * 100 = 19%.
Thus, the percent rate of change of y for each unit of x is 19%.