# Calculus-Modeling Equations

posted by .

An unknown radioactive element decays into non-radioactive substances. In 420 days the radioactivity of a sample decreases by 39 percent.

1.What is the half-life of the element?

2.How long will it take for a sample of 100 mg to decay to 46 mg?

• Calculus-Modeling Equations -

A(t)= Ao* (1/2)^(t/h)
where h is the half life.
A/Ao = 1-0.39 = 0.61
0.61 = (1/2)^(420/h)
log 0.61 = (420/h) log (1/2)
420/h = 0.71312
h = 589 days

When 100 mg becomes 46 mg of radioactive material, A/Ao = 0.46
0.46 = (1/2)^(t/589)
t/589 = log(0.46)/log(0.50)= 1.1203
t = 660 days

• Calculus-Modeling Equations -

jh

## Similar Questions

1. ### math

You have just isolated a new radioactive element. If you can determine its half-life, you will win the Nobel Prize in physics. You purify a sample of 2 grams. One of your colleagues steals half of it, and eight days later you find …
2. ### Chemistry

A radioactive element has a half-life of 6.41 days. What percent of the original sample will be left after 15.0 days?
3. ### math

An unknown radioactive element decays into non-radioactive substances. In 100 days the radioactivity of a sample decreases by 64 percent. a)(a) What is the half-life of the element?

5. ### Science

When Marie Curie isolated uranium from pitchblende, she realized that the pitchblende was more radioactive than the uranium she had extracted. What did she conclude about her observations?
6. ### Engineering Math

An unknown radioactive element decays into non-radioactive substances. In 120 days the radioactivity of a sample decreases by 59 percent. What is the half life of the element?
7. ### PRe calc story problem!!

A radioactive element decays exponentially according to the function Q(t) = Q0ekt .If 100 mg of the element decays to 25 mg in 12 days, find the half-life of the element.
8. ### pre calc

A radioactive element decays exponentially according to the function Q(t) = Q0ekt .If 100 mg of the element decays to 25 mg in 12 days, find the half-life of the element. please help
9. ### Science

An element has a half-life of 30 years. If 1.0 mg of this element decays over a period of 90 years, how many mg of this element would remain?
10. ### math

An element has a half-life of 30 years. If 1.0 mg of this element decays over a period of 90 years, how many mg of this element would remain?

More Similar Questions