Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=570(1.01)^x
The exponential function is given by y = 570(1.01)^x.
This function represents growth because the base of the exponent (1.01) is greater than 1.
To determine the percentage rate of increase, we can compare two values of y at different values of x.
For example, let's compare y when x = 0 and when x = 1:
When x = 0:
y = 570(1.01)^0
y = 570 * 1
y = 570
When x = 1:
y = 570(1.01)^1
y = 570 * 1.01
y ≈ 575.7
The percentage rate of increase is found by taking the difference between the two values and dividing by the initial value, and then multiplying by 100:
Rate of increase = ((575.7 - 570) / 570) * 100 ≈ 0.98%
Therefore, the exponential function represents a growth of approximately 0.98% per unit change in x.