how to do half life science problems?

Question

i got an ACT tormorrow and i need to remember how to do those.

Answer 1

Well, half-life problems come up whenever the rate of decay of a measured property is equal to the instantaneous value of the property. ie dy/dt = ky (k is negative)

The solution to this linear differential equation is:

y(t) = Ae^(kt)

A is typically the value of y at t=0, while k is the time constant. You are looking at a decay process, so k<0.

So if I tell you the half-life of pretzels in my house is 1700 minutes and I had 100 pretzels 24 hours ago:

y(1/2 life) = 0.5 * 100 = 100 * e^(k*1700)
k = (ln(50/100))/1700 = -0.000408
Therefore;
y(24hrs) = 100 * e^(-0.000408 * 24 * 60) = 55.6 pretzels

ie Not quite half thru. Better stock up anyway,

Hope this helps.

Answer 2

If the half-life of C 14 is 5700 years and the expectation is that 20% of the carbon in a speciman should be C 14... If it is only 10% there is only HALF. That means that it is 5700 years old. If it is only 5% it is half of the half. Therefore, it is two half-lives old = 11,400. Look at the residual compared to the original amount. Determine what portion is left. (Ex: Started w/ 10 gr., have 1.25 gr... Okay, 10/2=5 you'ld have 5 gr. after 1 half-life. 5/2 = 2.5...2.5 gr. remain after 2 half-lives. 2.5/2=1.25 would be the number of grams of anything after 3 half lives. The speciman is 3 x (Its Half Life) old.