A quantity decreases by 30 each year for a period of 8 years

A quantity decreases by 30% each year for a period of 8 years. What is its percentage decrease over the 5-year period? Show your work by filling in the following table. yearly decay rate=____?

yearly decay factor=____?

8-year decay factor=____? (show calculation, rounded to 3 decimal places)

8-year decay rate=___? (to the nearest tenth of a percent.

Solution

% decrease over 5 year period = (1 - r)^5 = (1 - 0.3)^5 = 0.168 = 16.8%

Decay factor = ( 1 - r) = 1 - 0.3 = 0.7

8 year decay factor = ( 1-r)^8 = ( 1 -0.3)^8 = 0.057

8 year decay rate = r = 1 - 0.057 = 0.94 = 0.9