Posted by **kela** on Friday, November 9, 2012 at 6:00pm.

A sample of a radioactive substance decayed to 94.5% of its original amount after a year. (Round your answers to two decimal places.)

(a) What is the half-life of the substance?

(b) How long would it take the sample to decay to 65% of its original amount?

- calculus -
**Reiny**, Friday, November 9, 2012 at 6:06pm
general equation

amount = starting (1/2)^(t/k) , where t is the time and k is the half-life period

a)

.945 = 1(.5)^1/k

ln .945 = (1/k)ln.5

1/k = ln.945/ln.5

k = ln.5/ln.945 = 12.25 years

b)

.65 = (.5)^t/12.25

t/12.25 = ln.65/ln.5 = .621488..

t = 7.61 years

- calculus -
**Anonymous**, Friday, March 7, 2014 at 3:08am
A certain radioactive isotope decays at a rate of 2% per 100 years. If t represents time in years and y

represents the amount of the isotope left then the equation for the situation is y= y0e-0.0002t. In how many years will there be 93% of the isotope left?

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