Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

Question

y
=
65
(
1.03
)
x
y=65(1.03)
x

Answer 1

This exponential function represents growth because the base (1.03) is greater than 1.

To determine the percentage rate of increase, we can use the formula:

rate of increase = (new value - original value) / original value

In this case, the new value is y and the original value is 65. We can also write the exponential function as:

y = 65 * (1 + 0.03) ^ x

This shows that the rate of increase is 3% (0.03 as a decimal). Therefore, for every unit increase in x, the value of y increases by 3%.