Question

A factory was ordered to reduce the amount of pollution by 51% in two years with the same percent decrease each year. What is this percentage?

PLEASE HELP!!!

Answer 1

30%

Explanation:

You want the percentage reduction each year that will result in a reduction of 51% over two years.

Growth factor

The growth factor is 1 added to the growth rate. If the desired growth rate over 2 years is -51%, then the growth factor for that period is ...

1 -51% = 0.49

If the growth factor is the same for each of two years will be ...

(1 +r)² = 0.49 . . . . . . . where r is the growth rate each year

Growth rate

Solving for r gives ...

1 +r = √(0.49) = 0.7

r = 0.7 -1 = -0.3 = -30%

The required growth rate each year is -30%.

The pollution must be reduced by 30% each year for 2 years.

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