Find the constant k
- Thread starter Neko san
- Start date
I believe that n is the inital amount of the substance, y is the final amount, k is the constant you're solving for, e is a constant (approx. 2.718), and t is time the substance is decaying. I'm not entirely sure about all this, so you should probably check with another source about this on your own. Okay, so you know that after 32 years (32 is your t-value), n will be half of what it was, or (n/2), so first plug that in for y, your final amount of the substance.
(n/2) = n*e^(k*32)
Then, I would move the n to the left side of the equation:
(n/2)/n = e^(k*32)
the n's cancel:
(1/2) = e^(k*32)
Then, take the natural log of both sides to get rid of the e:
ln(1/2) = k*32
Divide both sides by 32 to solve for "k":
[ln(1/2)]/32 = k = (approx.) -0.02166
http://tinyurl.com/2ymorj
You can tell this is probably right, because k is negative, and so it means the substance is decreasing in size, or decaying. Also, just for future reference, the equation: y = n*e^(k*t) is called the logistics equations, and it can model either growth or decay, depending on the sign of k. I think.
(n/2) = n*e^(k*32)
Then, I would move the n to the left side of the equation:
(n/2)/n = e^(k*32)
the n's cancel:
(1/2) = e^(k*32)
Then, take the natural log of both sides to get rid of the e:
ln(1/2) = k*32
Divide both sides by 32 to solve for "k":
[ln(1/2)]/32 = k = (approx.) -0.02166
http://tinyurl.com/2ymorj
You can tell this is probably right, because k is negative, and so it means the substance is decreasing in size, or decaying. Also, just for future reference, the equation: y = n*e^(k*t) is called the logistics equations, and it can model either growth or decay, depending on the sign of k. I think.