An element with mass 140 grams decays by 21.6% per minute. How much of the element is remaining after 20 minutes, to the nearest 10th of a gram?

Answer 1

Po = 140 grams= initial amount

21.6% per minute decay rate=- .216 = rate of change = r

how much is left after 20 minutes?

use the formula

A=Poe^rt where t= number of minutes=20,e=an irrational constant = about 2.718281828, r=.216

A=140e^-.216(20) = 140e^-4.32 = about 1.862 grams after 20 minutes

if decay is continuous

using a calculator

but most people would go with the following solution

time t Amount

0 140

1 .784(140)

2 .784^2(140)

3 .784^3(140)

...

t .784^t(140)

...

20 .784^20(140) = 1.078 grams

if it decays .216 per minute, 1-.216 is left each minute= .784

A=P(1-r/n)^nt is the general formula where decay occurs n times per minute. if n=1, then

= 140(1-.216/1)^(1)(20) = 140(.784^20) = 1.078