Question

The radioactive substance cesium-137 has a half-life of 30 years. The amount A (t)(in grams) of a sample of cesium-137 remaining after t years is given by the following exponential function. A(t)=934(1/2)^t/30
Find the amount of the sample remaining after 40 years and after 100 years.
Round your answers to the nearest gram as necessary.
Amount after 40 years :
Amount after 100 years :

Answer 1

Rather than use that formula, look at the attachment and use the 4th equation.

Ending Amount = Beginning Amount / 2^n
where "n" is the number of half-lives.  "n" = elapsed time / half-life
(Is 934 the beginning amount? Let's say it is.)

for 40 years, n=40/30 = 1.3333333...
Ending Amount = 934 / 2^1.3333333...
Ending Amount = 934 / 2.5198420998
Ending Amount = 370.66 grams

for 100 years, n=100/30 = 3.333333 ...
Ending Amount = 934 / 2^ 3.333333 ...
Ending Amount = 934 / 10.0793683992
Ending Amount = 92.66 grams

Source:
http://www.1728.org/halflife.htm