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Question

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

1.Find a function
m(t) = m02−t/h
that models the mass remaining after t years.

2.Find a function
m(t) = m0e−rt
that models the mass remaining after t years. (Round your r value to four decimal places.)

3.How much of the sample will remain after 61 years? (Round your answer to one decimal place.)

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

Answer 1

1.Plug in the given information into the equation your teacher gave you. Since the half life is 30 years, then the the remaining mass is half of what we started with when we plug in the information your teacher gave.

0.5m₀=m(30years)=m₀(2)^{-30 years/h}

Divide both sides by m_0, and solve for h. You can do this by taking log base 2 of both sides and with some good algebra that will instil hard work with you. 

2. This is the same problem type as 1, but this time when you have to use the log it must be natural log, that is log base e or as it is commonly denoted on calculators "ln".

 

I hope to answer more of your questions soon.

-cldp