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?

Question

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

200 = 320e^-.051t, solve for t

20/32 =5/8 = e^-.051t

nake natural logs

ln(5/8) = -.051t

t = ln(5/8)/-.051 = about 9.215757

= about 9.2 minutes

rounded to nearest 1 decimal