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Radium decays by about $35 \%$ every 1000 years. How much of a 75 lb sample remains after (a) 2000 years (b) 10,000 years?

(a) $31.6875 \mathrm{lb}$(b) $1.00971 \mathrm{lb}$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Campbell University

McMaster University

Idaho State University

Lectures

02:18

Radioactive Carbon 14 deca…

01:46

(a) The half-life of radiu…

02:32

(a) Given that the decay c…

04:33

If the half-life of radium…

05:09

Radioactive Decay The half…

Radioactive Decay Radioact…

If we want to figure out how much of this radium is going to be left after two and 10,000 years, the first thing we can do is try to go ahead and set up our equation and we'll have to treaty a little bit differently. Since our units for a rate isn't just years, it's thousands of years. So the base equation we can still right the same. But now T is going to have to be in the 1000 of years. So that means for a over here who just divided by 1000. So that gives us t is two and then over here for 10,000, we divided by 1000. So that gives us t is 10. So then once we get our equation set up here, we just blow to and tendon and we'd be done. So our initial amount is just gonna be 75. Our rates are well, since it's DK, that means our is negative. And then we just divide 35% by 100 to turn it into a decimal just zero point 35 So now we can go ahead and combine those so one minus 10.35 is 0.65 and I would just plug two and 10 and two here and we'd be done. So P of two is going to be 75 times 0.65 squared, which gives us something around 31 point. And I'm just going around this to two decimal points of a 69 pounds. And then over here we plug in 10 BP of 10, so 75 times 0.65 race to the 10th, 0.658 10 times 75. And that gives us something around 1.1 pounds. So that is how much radium we should have after two and 10,000 years.

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