An isotope of sodium has a half-life of 20 hours. Suppose an initial sample of this isotope has mass 10 grams.The amount of the isotope (in grams) remaining after t hours is given by ? (We're assuming exponential decay here. Use the exponential decay function).

Question

immings · Answer

e^-tm

anonymous · Answer

Is that the function we're suppose to use? The choices are:

a. 10(1.035264924)^t 
b. 10(.965936329)^t 
c. 20(1.071773462)^t 
d. 20(0.9330329915)^t 
e. None of these

immings · Answer

Ok I won't use that e (which is an inverse function of the ln( button but I won't get into that. So basically you know your numbers Your half life is your t, and your mass would be the other value in front of the brackets, so you've narrowed down your answers to two possible ones. So trying A) when you put in the t = 10 and t = 20 hours the value increases
but when you try this with B) the values for t = 10 and t = 20 goes down. therefore you could say that B is the correct answer because half life you are losing the sodium. where as in A you are gaining mass.

immings · Answer

Hope this helps!

johnweldon1993 · Answer

Lol he is correct...

In both C and D ...the first number where your original mass would go should be 10...but instead it is 20....so automatically they are out...

In A ...inside the parenthesis we have (1.035264924)^t    if we raise that to any power...it will get bigger...hence when you multiply it to the 10 you have in front...THAT will get bigger...Doesn't make sense right? This is supposed to be half life and decaying sodium..and yet the mass is getting bigger...

So we are left with B

anonymous · Answer

Thanks guys!