Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease per unit of xx, to the nearest tenth of a percent.y, equals, 400, e, start superscript, 0, point, 1, 1, 5, x, end superscripty=400e 0.115x
Question
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease per unit of xx, to the nearest tenth of a percent.y, equals, 400, e, start superscript, 0, point, 1, 1, 5, x, end superscripty=400e 0.115x
Solution
The given function is y = 400e^(0.115x).
This is an exponential function, and we can identify whether it represents growth or decay by looking at the exponent of e.
In this case, the exponent is 0.115x. Since 0.115 is positive, this function represents exponential growth.
To find the percentage rate of increase per unit of x, we convert the growth rate from its decimal form to a percentage.
0.115 in decimal form is equivalent to 11.5% in percentage form.
So, the function represents a growth of 11.5% per unit of x.
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