Question

Calculate the percentage rate of increase per unit of x, to the nearest tenth of a percent, for the function y = 1200(0.86)^4x when x increases by 1 unit.

A) 14.9%
B) 12.4%
C) 10.9%
D) 17.1%

Answer 1

To find the percentage rate of increase for the function y = 1200(0.86)^4x when x increases by 1 unit, calculate y for x and x + 1, find the difference, and then divide by the original y. Multiply the result by 100 to obtain the percentage increase.

Step-by-step explanation:

To calculate the percentage rate of increase per unit of x for the function y = 1200(0.86)^4x when x increases by 1 unit, we first need to find the value of y for x and then for x + 1. We then use these two values to find the percentage increase.

Let's calculate y for x:
y = 1200(0.86)^(4x)

Now, calculate y for x + 1:
y = 1200(0.86)^(4(x + 1))

After calculating those two values, we subtract the original y from the new y and then divide by the original y. Finally, multiply by 100 to get the percentage.

Percentage rate of increase = ((New Value - Original Value) / Original Value) x 100%

Applying the values:

Original y = 1200(0.86)^(4x)

New y = 1200(0.86)^(4(x + 1))

Percentage rate of increase = ((New y - Original y) / Original y) x 100%