Half-Life Formula #12-13

Question

Assume that my lawn is encroaching my garden and reduces my space, on average, by 7% each year.

 Approximately how many years before the garden space has been cut in half?

(Round to the nearest tenth.)

 If the garden started out at 600 square feet, approximately how many square feet will there be in 13 years?

(Round to the nearest whole number.)

Answer 1

A = a(0.93)^x            Reducing by 7% means that 93% remians

 

0.5a = a(0.93)^x

0.5 = 0.93^x

ln 0.5 = ln 0.93^x

ln 0.5 = x ln 0.93

-0.693147181 ≈ x (-0.0725706928)

9.55133752 ≈ x

 

Your lawn is gone in 9.6 years.

 

For thirteen years calculate

 

A = 600(0.93)¹³