SOLUTION: The half-life of radium-226 is 1600 years. Suppose we have a 21-mg sample. (a) Find a function m(t) = m0^2−t/h that models the mass remaining after t years. m(t) =

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The half-life of radium-226 is 1600 years. Suppose we have a 21-mg sample. (a) Find a function m(t) = m0^2−t/h that models the mass remaining after t years. m(t) =       Log On


   

Question 979491: The half-life of radium-226 is 1600 years. Suppose we have a 21-mg sample.
(a) Find a function
m(t) = m0^2−t/h
that models the mass remaining after t years.
m(t) =
(b) Find a function
m(t) = m0^e−rt
that models the mass remaining after t years. (Round your r value to six decimal places.)
m(t) =?mg
(d) After how long will only 18 mg of the sample remain? (Round your answer to the nearest year.)
t =?years
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
I'm looking at your function formulas very carefully. The one in (a) means nothing because either you are not writing it correctly or you miscopied what you saw. The function formula in (b) needs to have grouping symbols in the text and the exponentiation symbols needs to be placed correctly.

Your decay function formula should be m(t)=m[o]e^(rt), although most of the time people will use k instead of r. The rendered form will appear m%28t%29=m%5Bo%5De%5E%28rt%29.

See my other solution posting for today to understand how to find what you want from this type of formula (similar for growth equations as well as for decay equations.). You can take log of both sides, solve for r, and use the half-life information to get the value of r. Similarly you can solve for t and use whatever other values are needed.