SOLUTION: Solve the problem.
Use the formula N = Iekt, where N is the number of items in terms of the initial population I, at time t, and k is the growth constant equal to the percent of
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Question 301769: Solve the problem.
Use the formula N = Iekt, where N is the number of items in terms of the initial population I, at time t, and k is the growth constant equal to the percent of growth per unit of time. A certain radioactive isotope decays at a rate of 0.275% annually. Determine the half-life of this isotope, to the nearest year. (
182 years
3 years
252 years
109 years
Thank you
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Use the formula N = Iekt, where N is the number of items in terms of the initial population I, at time t, and k is the growth constant equal to the percent of growth per unit of time.
:
I think the formula should be N = I*e^(kt)
Find the growth constant, k using t = 1 yr
I = 1
then
N = 1 - .00275 = .99725 remaining after 1 hr
:
e*k = .99725
k*ln(e) = ln(.99725)
k = -.00275, (decay is negative growth)
:
A certain radioactive isotope decays at a rate of 0.275% annually.
Determine the half-life of this isotope, to the nearest year.
N = .5
I = 1
k = -.00275
:
1*e^(-.00275t) = .5
-.00275t*ln(e) = ln(.5)
-.00275t = -.693
t =
t = 252.05 yrs is the half life of the isotope
:
:
Check solution on a calc
enter e^(-.00275*252) = .500; confirms our solutions
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