## 229. Math Puzzle $6 / 84$

A company has set itself the goal of reducing its energy consumption by 5 percent of the previous year's value each year.

After how many years will the energy consumption be only about 77 percent of the initial value?
At the beginning, the energy consumption is $A$ (kW):

after one year, it is only $0.95 A$

after two years, only $(0.95)^{2} A=0.9025 A$

after three years $(0.95)^{3} A=0.8573 A$
after four years $(0.95)^{4} A=0.8145 A$

after five years $(0.95)^{5} A=0.7737 A ; 77.4$ percent of $A$

After about five years, the consumption is only 77 percent of the initial value.