SOLUTION: The rate of decay of radium is said to be proportional to the amount of radium
present. If the half-life of radium is 1700 years and there are 400 grams on hand now, how
much rad
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Question 1194522: The rate of decay of radium is said to be proportional to the amount of radium
present. If the half-life of radium is 1700 years and there are 400 grams on hand now, how
much radium will be present in 900 years given the exponential decay equation, 𝑦 = Ce^kt.
what is the value of e^k, and how much radium will be present in 845 years.
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Half-life information,
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
formula is f = p * e ^ (kt)
half life formula is 1/2 = e ^ (1700k)
take the natural log of both sides of the equation to get:
ln(1/2) = ln(e^1700k)
this becomes:
ln(1/2) = 1700k * ln(e) which becomes ln(1/2) = 1700k
solve for k to get:
k = ln(1/2)/1700 = -4.07733636 * 10^-4
confirm by replacing k in the original equation to get:
f = p * e ^ (-4.07733636 * 10 ^ -4 * 1700) = .5
this confirms the value of k is correct.
if the present value is 400, the value will be 200 in 1700 years.
f = 400 * e ^ ((-4.07733636 * 10 ^ -4 * 1700)) = 200.
value of k is confirmed again.
in 900 years, the value will be 400 * e ^ (-4.07733636 * 10 ^ -4 * 900) = 277.1348678.
in 845 years, the value will be 400 * e ^ (-4.07733636 * 10 ^ -4 * 845) = 283.4199231.
the value of e^k is equal to e^ (-4.07733636 * 10 ^ -4) = .9995923495.
not sure why you'd want this because the formula required is e ^ (kt).
e^k means that t = 1.
i graphed the equation.
the equation graphed is y = e ^ (-4.07733636 * 10 ^ -4 * x)
it is shown below.
let me know if you have any questions.
theo
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