A bacteria decomposes at a rate proportional to the amount present. If the bacteria has a half-life of 30 minutes, what percent of the original amount is expected to remain after 54 minutes.

Question

psymon · Answer

Well, we have the formula Y = ce^(kt). I know some people know different letters, but yeah. So one quick way to solve these is if you know the half-life, you can find k immediately. 
$$k=\frac{ -\ln2 }{ half-life }$$so this means that -ln2/30 is your k. Now since we have an original amount of 100%, or simply 1. This means C is also 1 because at t = 0, C is the same as the original amount. So with all that information we can set this up and solve for the amount remaining after 54 minutes:
$$y=e ^{\frac{ -54\ln2 }{ 30 }}$$

anonymous · Answer

Thank you! How did you arrived with that equation of k?

anonymous · Answer

wow

anonymous · Answer

$$A=\left(\frac{1}{2}\right)^{\frac{t}{30}}$$ put 
$$t=54$$ and see what you get

anonymous · Answer

^ That's much easier to remember tbh.

anonymous · Answer

a body weighing 45 lbs. is heated to a temperature of 300 degrees. then at t=0 it is plunged into 100 lbs. water at a temperature of 50 degrees. given that the specific heat of the body is 1/9, find the formula for the temperature T of the body during it's cooling.