General

@LeeJoon: Yup.

First substitute 0.33n in for m, cancel the n's, then take the ln of both sides, which due to exponent rules allows the 8 to multiply in front of the ln, then since e^ln(c) = c, put both sides as powers of e, leaving the last line.

[quote=LowWillpower]The equation would be mass(t) = original mass * (r)^t where r is the rate of decay. Lets call mass m and original mass n

m = n* r^t, we know when m = 0.33 *n; t = 8, so the rate of decay can be solved. 0.33n = n * r^8
0.33 = r^8
ln(0.33) = 8*ln(r)
ln(0.33)/8 = ln (r)
r = e^(ln(0.33)/8)

Once you find r, you can solve for when m = 0.5 n for t (using the same kinds of exponential rules) to give the half life.

@Play3r can you explain those steps?

Ok so far looks like LowWillpower and xLiliumn is the only one who actually helped me get a seemingly correct answer.

@xLiliumn I'm reading your explanation but I'm having a bit of trouble trying to comprehend. My brain is fried right now lol.

[quote=LeeJoon]Raising rewards up to 2 bil or 20k nx for a faster solution. The first one is the bismuth-210 one and the second question is
A car engine runs at a temperature of 190 ferenheit. When the engine is turned off, it cools according to newtons law of cooling with constant k=0.0342, where the time is measured in minutes. Find the time needed for the engine to cool to 90 degrees if the surrounding temperature is 60 degrees[/quote]
Newtons law of cooling is T = Ta + (To - Ta)*e^(-kt) Where Ta is ambient temperature and To is initial temperature. Plug in for T = 90 and solve for t

90 = 60 + (190-60)*e(-0.0342)*t
30/130 = e(-0.0342t)
ln(30/130) = -0.0342t
t = ln(30/130)/(-0.0342)

Well first, you know that 2a+2b>a^2+b^2
This said, the statement is false because should you put a=2 andb=3, it would equal 10>13, which isn't true.

Raising rewards up to 2 bil or 20k nx for a faster solution. The first one is the bismuth-210 one and the second question is
A car engine runs at a temperature of 190 ferenheit. When the engine is turned off, it cools according to newtons law of cooling with constant k=0.0342, where the time is measured in minutes. Find the time needed for the engine to cool to 90 degrees if the surrounding temperature is 60 degrees

[quote=LeeJoon]Ok.. well then let's forget that one. What about this problem?
Sample bismuth-210 decayed to 33% of its original mass after 8 days.
A) Find half-life
B) Find mass after 12 days.
How would I go about this?

The person who helps me answer these extra credit questions correctly has a choice of 1bil mesos or 10k nx[/quote]
The equation would be mass(t) = original mass * (r)^t where r is the rate of decay. Lets call mass m and original mass n

m = n* r^t, we know when m = 0.33 *n; t = 8, so the rate of decay can be solved. 0.33n = n * r^8
0.33 = r^8
ln(0.33) = 8*ln(r)
ln(0.33)/8 = ln (r)
r = e^(ln(0.33)/8)

Once you find r, you can solve for when m = 0.5 n for t (using the same kinds of exponential rules) to give the half life.

To find the mass after 12 days just plug in t = 12 and solve for m relative to n.

plug in a = 0, b = anything, contradiction

Ok.. well then let's forget that one. What about this problem?
Sample bismuth-210 decayed to 33% of its original mass after 8 days.
A) Find half-life
B) Find mass after 12 days.
How would I go about this?

The person who helps me answer these extra credit questions correctly has a choice of 1bil mesos or 10k nx

[quote=LeeJoon]That's what i did but the professor just said that I plugged in numbers and did not prove for arbitrary numbers or something like that. I am completely stumped..[/quote]

You can't prove that's true because there is no solution.
http://www.wolframalpha.com/input/?i=ab%3E%28a%5E2%2Bb%5E2%29%2F2

for all real numbers a and b?
your prof be trollin

That's what i did but the professor just said that I plugged in numbers and did not prove for arbitrary numbers or something like that. I am completely stumped..