Question

Lead-210 also has a radioactive decay rate. Its half-life is 22 years. What is k, its exact decay rate? k = _____ If we assume that we begin with an initial amount of 1000g of lead, write a function that approximately models the lead-210 at time, t, in years. Round k to 2 significant figures for the function. m(t) = _____ Fill in the t-values and answer the questions with function equations. Include units. Be exact. It might be easier without your calculator. Exactly how much will remain after 44 years? m(_____) = _____ Exactly how much would there have been 22 years ago? m(_____) = _____ Exactly how much will remain after 110 years? m(_____) = _____ When will there be 500g of lead? Include units. t = _____ When will there be 125g of lead? Include units. t = _____ When was there 4000g of lead? Include units. Graph the function. t = _____

Answer 1

Half-life t_1/2 = 22 years

t_1/2 = 0.6931/k

k = 0.6931/22

k= 0.0315

The function of decay

N = N_oe^-kt

After 44 years

Here N_o=1000 gram and k = 0.032

N = 1000e^-0.032x44

N = 244.63 grams

22 years ago

Here N=1000 gram and k = 0.032

1000= N_oe^-0.032x22

N₀ = 2021.84 grams

After 110 years

Here N_o=1000 gram and k = 0.032

N = 1000e^-0.032x110

N = 29.6 grams

To find t for 500 gram

500 = 1000 e^-0.032xt

0.5 = e^-0.032t

ln 0.5 = -0.032t

t = 21.66 years

to find t for 125 g

125 = 1000 e^-0.032xt

0.125 = e^-0.032t

ln 0.125 = -0.032t

t = 64.98 years

.. 4000 2000 . -40 -20 20 40 60 80 100 120 ..-2000....