The amount of radioactive substance after 38 days

[Pushoam]

Homework Statement

Homework Equations

The Attempt at a Solution

Is there anyway to choose the correct option without solving it?

$\lambda = \frac { 0.693 } { t_{\frac 1 2}}$
[/B]
$N = N_0 e^{- 0.693 {\frac { t } { t_{\frac 1 2 }}}}$

$N = 10.24 e^{- \frac { 0.693 * 38 } { 3.8} } = 10^{-2} ~ gm$So, the correct option is (b).

Is this correct?

 

[symbolipoint]

Why the raised dot between those digits? If to mean decimal point, that is not the way to show it.
Half-life, 3.8 days;
Want how much after 38 days;
Begin with 10.24 grams

If model is for exponential decay, then A=10.24*e^(-k*t).
Find k using half-life information.
(1/2)=1*e^(-k*3.8)
(1/2)=e^(-3.8k)
ln(1/2)=ln(e^(-3.8k))
ln(1/2)=-3.8k*1
k=-ln(1/2)/3.8
k=ln(2)/3.8
k=0.1824

Revise for the more specific decay equation:
A=10.24*e^(-0.1824t)

How much remaining after 38 days?
Let t=38 and evaluate A.

 

[mjc123]

38 days is 10 half-lives. 2^10 = 1024. 10.24/1024 = 0.01.

 

[Pushoam]

Why the raised dot between those digits? If to mean decimal point, that is not the way to show it.

It is the symbol of multiplication. Please, see the keyboard for this. You, too, have used it in the following expression,

A=10.24*e^(-k*t).

k=ln(2)/3.8

I have written $\lambda$ instead of k.
The above is nothing but, k = 0.693 /t_½.

 

[symbolipoint]

It is the symbol of multiplication. Please, see the keyboard for this. You, too, have used it in the following expression,
I have written $\lambda$ instead of k.
The above is nothing but, k = 0.693 /t_½.

I looked at the linked document you posted in the beginning post. There was a raised dot but that is to be used to signify multiplication. We want the character to be at the botton of the digits levels to read it as a decimal point. If I use a raised dot, I use it as a multiplication operation. That is the normal, common usage. The middle quoted passage shows the asterisk also often used for multiplication, and common and usually understood when using plain text to write an algebraic expression; it might appear as a raised dot, or it might appear exactly the asterisk. The 10.24 shows the decimal point, and the "three point eight" as the decimal number should be written as 3.8 (notice the dot at the bottom-level).