Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y
=
65
(
1.03
)
x
y=65(1.03)
x
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%.
To determine whether the change represents growth or decay in the given exponential function, we need to examine the value of the base of the exponential expression, which is 1.03 in this case.
If the base, in this case 1.03, is greater than 1, the function represents growth. If the base is less than 1, the function represents decay.
In this case, the base 1.03 is greater than 1, so the function represents growth.
Now let's determine the percentage rate of increase. The base 1.03 represents a 3% increase for each x value.
Therefore, the percentage rate of increase is 3%.