# word problem

posted by
**Jen**
.

The half life of cesium-137 is 30 years. Suppose we have a 10-g sample.

a)Find a function that models the mass remaining after t years.

b)How much of the sample will remain after 80 years?

c)After how long will only 2 g of the sample remain?

Thanks

(a) M(t) = mass of Cesium-137 at time t, in years = Mo* 2^(-t/30)

Mo is the initial mass of 10 g.

2^(-t/30) means 2 to the -t/30 power

(b) Plug in t = 80 and see that you get for M

(c) Set M = 2 and see what you get for t. Hint: take logs of both sides of:

2 = 10 * 2^(-t/30)

(0.2) = 2^(-t/30)