SOLUTION: Hi there, I have an exam today and I was doing a practise exam where I came across this question and was unable to solve it. Could one of the tutors please help me with it, I'd be

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Question 204550: Hi there, I have an exam today and I was doing a practise exam where I came across this question and was unable to solve it. Could one of the tutors please help me with it, I'd be more than grateful!!!!
Scientists have 50g of a radioactive element that decomposes with a half-life of 15 seconds. (3 marks:1 mark each)
a) Write an equation that predicts the amount of the element remaining as a function of time.
b) How much of the element would remain after 2 minutes?
c) How long would the element take to decompose to the point where there is only 0.01g remaining?
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
Scientists have 50g of a radioactive element that decomposes with a half-life of 15 seconds. (3 marks:1 mark each)
a) Write an equation that predicts the amount of the element remaining as a function of time.
P = Ce^(kt)
25 = 50e^(k*15)
25/50 = e^(k*15)
1/2 = e^(k*15)
ln(1/2) = 15k
ln(1/2)/15 = k
Your equation then:
P = 50e^[(ln(1/2)/15)t]
.
b) How much of the element would remain after 2 minutes?
2 minutes = 2*60 = 120 secs
plug it into the equation:
P = 50e^[(ln(1/2)/15)t]
P = 50e^[(ln(1/2)/15)120]
P = 50(.00390625)
P = .195 grams
.
c) How long would the element take to decompose to the point where there is only 0.01g remaining?
0.01 = 50e^[(ln(1/2)/15)t]
0.0002 = e^[(ln(1/2)/15)t]
-8.5172 = (ln(1/2)/15)t
-8.5172/(ln(1/2)/15) = t
184.32 secs = t