An element with a mass of 320 grams decays by 5.1% per minute. To the nearest tenth of a minute, how long will it be until there are 200 grams of the element remaining?

Answer 1

Each minute the mass of 320 grams will be reduced by 5.1% and will thus be 94.9% of its previous value. After 1 minute it will be 320 * 0.949 ... after n minutes it will be 320 * 0.949^n.

To find at what n, it will be 200, equate 320 * 0.949^n to 200 and solve for n:

320 * 0.949^n = 200

0.949^n = 0.625

log 0.949^n = log 0.625

n * log 0.949 = log 0.625

n = log 0.625/log 0.949 = 8.98 ~ 9 minutes