A quantity decreases by 3% for each of 10 years. What is its percentage decrease over the 10-year period? (Round your answer to two decimal places.)

Answer 1

If we decrease something by 3%, we are left with 97%, right?

97¹⁰ = 0.7374 = 73.74%

100 - 73.74 = 26.26%

Answer 2

Hi Kimberly,

Using the equation y = a (b)^t, we know that t= 10. (Equation 1)

Also, since the yearly decrease is 3% (0.03), we know that b = 1-0.03 = 0.97

So Equation 1 becomes:

y_{10 years} = a (0.97)¹⁰ (y_{10 years} means the final value after 10 years)

= 0.7374a

To find the percent decrease after 10 years, you want to divide how much it decreased by the original amount

This can be written (a-y_{10 years})/a,

which becomes (a-0.7374a)/a

This simplifies to (1-0.7374), or 0.2626

That's a 26.26% decrease.

Hope that helps, and let me know if you have questions!

Stephanie