A quantity decreases by 9% for each of 10 years. What is its percentage decrease over the 10-year period? (Round your answer to two decimal places.)

Answer 1

You get the same percentage reduction using any original amount, Try 100 as the original amount then

100- .09(100) = 100(1 -.09) = 100(.91) = 91 after one year, 9% reduction after one year

91(.91) =82.81 .1719 % reduction after two years

91(.91)(.91) = 75.36 .24.64% reduction after three years

91(.91)^3 = 68.57 .31.43% reduction after four years

91(.91)^9 = 38.94 .61.06% reduction after ten years

after 10 years 100(.91)^10 = about 38.94, 61.06% reduction

use a calculator to find a^b = .91^10

if it's reduced by 9%, 91% is left after each year's reduction

A(.91)^10 = A(.3894) which is 38.94% of what it was 10 years earlier and 61.05% less than 10 years earlier

1-.38904 = .6105