# Calculus

posted by Anonymous

Radius decays at a rate of that is proportional to its mass, and has a half-life of 1590 years. If 20 g of radium is present initially, how long will it take for 90% of this mass to decay?

1. Reiny

so you want 10% to remain (the 20g is actually not relevant)

solve
.1 = (1/2)^(t/1590)
log .1 = log (.5^(t/1590))
t/1590(log .5) = log .1
t/1590 = log .1/log .5
etc.

let me know if didn't get t = 5282

## Similar Questions

1. ### physics

A building has become accidentally contaminated with radioactivity. THe longest lived material in the building is strontium-90 (atomic mass of 90 Sr 38 is 89.9077). If the building initially contained 5.0kg of this subtstance and the …
2. ### Math - Exponential Decay

Radium decays exponentially. Its half-life is 1,690 years. How long will it take for a 50-gram sample of radium to be reduced to 5 grams?
3. ### Pre Calculus

Radium-221 has a half-life of 30 s. How long will it take for 95% of a sample to decay
4. ### calculus

The rate at which an amount of a radioactive substance decays is modeled by the differential equation dA/dt = kA, where A is the mass in grams, t is the time in years, and k is a constant. Answer the following. a) If a 100-gram sample …
5. ### Calculus

The half-life of Radium-226 is 1590 years. If a sample contains 100 mg, how many mg will remain after 4000 years?
6. ### Math

A radioactive substance decays according to the formula Q(t) = Q0e−kt where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a positive …
7. ### Math

A radioactive substance decays according to the formula Q(t) = Q0e−kt where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a positive …
8. ### MATHS

experiments show that radium disintegrates at a rate proportional to the amount of radium present at the moment . if half life is 1590 years what percentage will disappear in one year?
9. ### MATHS

please help me ...Experiments show that radium at rate proportional to the amount of radium present at the moment . if half life is 1590 years what percentage will disappear in one year ?
10. ### Calculus

The rate of decay is proportional to the mass for radioactive material. For a certain radioactive isotope, this rate of decay is given by the differential equation dm/dt = -.022m, where m is the mass of the isotope in mg and t is the …

More Similar Questions