Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=61(0.95)^x
The given exponential function is y = 61(0.95)^x.
To determine whether the change represents growth or decay, we need to examine the base of the exponential function. In this case, the base is 0.95.
Since 0.95 is less than 1, the base is between 0 and 1, indicating decay. Therefore, the change represents decay.
To determine the percentage rate of decrease, we can find the difference between consecutive values of y as x increases by 1.
Let's calculate the values of y for x = 0 and x = 1:
For x = 0:
y = 61(0.95)^0 = 61(1) = 61
For x = 1:
y = 61(0.95)^1 = 61(0.95) = 57.95
The difference between these two values is 61 - 57.95 = 3.05.
To express the percentage rate of decrease per unit increase in x, we divide the difference by the initial value and then multiply by 100.
(3.05/61) * 100 = 4.95%
Therefore, the percentage rate of decrease is approximately 4.95%.