The half-life of cesium-137 is 30 years. Suppose we have a 15-g sample.

Question

(a) Find a function m(t) = m₀2^−t/h

 that models the mass remaining after t years. 

m(t) = 

(b) Find a function m(t) = m₀e^−rt

 that models the mass remaining after t years. (Round your r value to four decimal places.) 

m(t) = 

 

 (c) How much of the sample will remain after 89 years? (Round your answer to one decimal place.) 

 

(d) After how many years will only 2 g of the sample remain? (Round your answer to the nearest whole number.) 

Answer 1

The equation provided matches all the variables you were given in the problem for part (a).

m(t) = m₀ * 2^-t/h

Here, m0 is the initial mass, t is the elapsed time, m(t) is the mass remaining after the elapsed time, and h is the half-life. You are given m0 and h, and t is your independent variable and m(t) is your dependent variable.

For part (b), the easiest way to approach it would be to just calculate a coordinate from the equation you developed in part (a). This is because these equations are calculating the same thing, but they are simply written differently. That is, plug in some arbitrary t value and calculate the m(t) value. Now, use those t & m(t) values, along with m0 (which is still the same) and plug it into the function they've given. Your only remaining variable is r.

For parts (c) and (d), this is simply plugging in and solving. In (c), you plug in the given value of t and solve for m(t). In (d), you plug in the given value of m(t) and solve for t. You can obviously use either the equation you developed in (a) or (b) since they are the same thing, but (b) may be cleaner to use algebraically.