Question

Suppose the amount of a certain radioactive substance in a sample decays from 3.80 mg to 2.50 mg over a period of 49.5 years. Calculate the half life of the substance.

Answer 1

Great! First identify the values of 'y', 'a' and 'r' and 't' from the given data

Answer 2

t is 49.5 years. r is rate I think this is the rate of decay which we are trying to find. and a is 3.80mg and y is 2.5mg

Answer 3

Good! Now plug the values in to the equation y = ae^(rt) and find the value of 'r' by using the log method

Answer 4

2.5 = 3.80e^(r49.5) is that done right? Do I need to put times after the r and before the t?

Answer 5

Yes you can put it, although it implies the same thing without it as well.

Answer 6

So log, right?

Answer 7

ye

Answer 8

yes*

Answer 9

log(2.50/3.80) =log(e^(r49.5)

Answer 10

-.1818435879 = log(e^(r49.5)

Answer 11

you have to take the natural log not which may be represented by ln on your calculator

Answer 12

when trying to remove 'e' we generally take the natural log and not the general log with base 10, because the natural log has a base e

Answer 13

I don't think my calculator has base 10

Answer 14

In the previous question the log values you gave were of natural log so you need to use the same buttons/method to find the log values here.

Answer 15

log(2.50/3.80) = -0.4187

Answer 16

-0.4187=log(e^(49.5t)=2.1*10^+1

Answer 17

so -0.4187/2.1*10^-1=r

Answer 18

-1.9*10^+2

Answer 19

I think I put the wrong positive on the 1 in the scientific notation after the log. I think it is suppose to be negative and then when I divide both sides it changes to negative.

Answer 20

which would make it -1.9. Is this right?

Answer 21

Half-Life = [Elapsed Time * log (2)] / log [begng amt / ending amt]
Half-Life = [49.5 years * .3010] / log [3.8 / 2.5]
Half-Life = 14.8995 / log [1.52]
Half-Life = 14.8995 / 0.1818435879
Half-Life = 81.94 years

Source:
http://www.1728.org/halflife.htm
(Formulas and a half-life calculator)

Answer 22

This asks Round your answer to 2 significant digits. Is that 8.2 * 10^ -1

Answer 23

Wow round that to 2 significant figures? (Gee that makes the answer somewhat inaccurate.)
81.94 rounded to 2 significant digits is 82.
and if you really need it in scientific notation, it is 8.2 x 10^1

Answer 24

Awesome thanks!

Answer 25

u r welcome

Answer 26

It does not say to write in scientific notation but it offers it. Do you think that I should put it in scientific notation of it is offered?

Answer 27

What do you mean by "it offers it"?

Answer 28

I am doing it in an online document and it has the scientific notation button.

Answer 29

Well I suppose you could. Usually with an answer such as 82, it is much easier to read as 82 and that is how I'd leave the answer,

Answer 30

Ok, thanks, again.

Answer 31

Okay - glad to help out.