Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y, equals, 420, left bracket, 1, point, 0, 4, right bracket, to the power x
y=420(1.04)^x
The given exponential function is y = 420(1.04)^x.
To determine whether the change represents growth or decay, we look at the base of the exponent, which is 1.04. If the base is greater than 1, it represents growth, and if it is less than 1, it represents decay. In this case, the base 1.04 is greater than 1, so the change represents growth.
To determine the rate of increase or decrease, we can look at the coefficient in front of the exponential part of the function, which is 1.04. This represents a 4% increase each time x increases by 1. Therefore, the percentage rate of increase is 4%.