Faster way to compute or estimate (1.02)^4?

[oreoandmilk2004]

I came across one of the OG problems that ask us to compute this (1.02)^4 as part of the answers, but it took me quite a bit after computing (1.02)^2 =1.0404 and then 1.0404 by 1.0404, I wonder if there is a faster way I can estimate this.

I would greatly appreciate any insight!

Thanks!

[tim]

a quick and pretty close estimate for raising a number really close to 1 to a higher power is to multiply the excess (in this case .02) by the power (.02*4 = .08) and add it to 1, so in this case 1.08 is a pretty good estimate..

[oreoandmilk2004]

Thanks, Tim. Would this technique only work for those numbers close to one? I wonder if we could expand this to other numbers...

[tim]

only for numbers close to 1 and relatively small powers. the farther you are from 1, and the larger the power is, the more the estimate will deviate from the correct answer..