Question

Suppose strontium-90 decays at a rate of 2 percent per year. (a) Write the fraction P of strontium remaining, as function of t, measured in years. (Assume that at time t=0 there is 100 % remaining.)
Answer: P(t) = (b) Estimate the half-life of strontium.
Answer:
Hint: Use your graphing calculator and the trace function. (Or use natural logarithms as in 1.9).(c) If presently there is 5.5 grams of strontium, estimate how many grams of the substance will remain after 11 years.
Answer:

Answer 1

Yes, you do

ds/dt = -.02 s

ds/s = -.02 dt

ln s = -.02 t + c

e^ln s = s = e^(c-.02t) = e^c e^-.02 t

e^c = C any old constant in the general solution

s = C e^-.02 t
when t = 0, s = Si the initial amount
so
s/Si = e^-.02 t
BUT that is P, the fraction remaining so we have part a

b) .5 = e^-.02 t
ln .5 = -.02 t = -.693
t = 34.7 years half life

in 11 years
s = 5.5 e^-.02*11
s = 4.41

Answer 2

Icicid