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Thorium 234 decays by about $3 \%$ every day. How much of a 10 lb sample remains after (a) 3 days, (b) 1 week (c) 30 days?

(a) $9.12673 \mathrm{lb}$(b) $8.07983 \mathrm{lb}$(c) $4.01007 \mathrm{lb}$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Campbell University

McMaster University

Baylor University

Idaho State University

Lectures

01:54

The mass $m(t)$ remaining …

02:11

The half-life of thorium-2…

01:47

A radioactive substance lo…

03:17

The half-life of the radio…

01:04

04:01

A sample of tritium-3 deca…

01:07

The half-life of plutonium…

03:16

A sample of tritium- 3 dec…

03:13

A radioactive material, su…

03:49

So if we want to figure out how much is left, given this 3% DK per day rate and an initial amount of £10 we can use that equation that we normally would use. So pft is equal to p not one plus our race, the tea. But we need to be careful about what our units are, so our rate constant over here is in days. So T needs to be in days. Um, and then once we figure this equation and plug everything in, all we need to do is just plug in. T is equal to that many days. So over here for a that would just be t 0 to 3 a week. There's seven days, so that would be seven and then for well, 30 days. That would just be teasing with 30. So our initial amount is 10 and there'll be one plus. Will DK's means it's decreasing so r R is negative, and then we convert 3% to attest most of the zero point, um 03 so negative 0.3 race the T. So this is going to be 10 times 0.97 race the teeth. Now we just need to plug 37 and 30 and and wait to be done. So p of three is going to be 10 times 0.97 raised to the third. So 0.97 cute times 10. That is going to give us something around 9.2. I shall just say 9.3 pounds. And I'm just going around these 22 decimal places. But you can round two more if you wish. Um, and then p seven is going to be so 10 times. 0.97 race. The 7.97 races seven times 10. So that will give us something around 8.8 pounds. And then lastly, we plug in 30 would be 10 times 0.97 rays to the 30 which is approximately £4.1. So that is how much we would have after each of those time intervals

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