1st year calc differential equation problems

I

ilovemathsomuch

New member
Joined
Feb 10, 2021
Messages
3
qde 1.jpgqde 2.jpg

Both of these seemed like half life questions so I used the differential equation dQ/dt=-kQ for each, solving for Q(t)=C*e^(-kt) (k as a constant representing half life of a substance). Despite this I can't even seem to get the one about writing the differential equation in question 2 right (shouldn't it be dQ/dt=-38Q ?). My answers for question one after solving for 0.34=1*e^(-k*580) were a) half life=1.86*10-3 and b) 444.4 days. Thanks in advance!
 
You're right, both are exponential decay/ half life problems, so nice job identifying the equation to use! But your half life for part a should be longer than 444 days since after 580 days it only decreased 34%. Your mistake is using the .34 in the equation. If it decreases by 34% then 66% remains. So use .66 instead!!

For the second question the "k" value is not 38. What you need to know is that k is just a constant, probably not a nice number, and definitely doesn't represent time. The 38 hours is a time (so should be plugged in for a t), specifically the time for the amount of material to decrease by 50%. You actually need to use the second equation for that question to find k since that equation is for the actual amount of material, not just the rate. You don't have any actual amounts, but you could just use any amounts as long as they represent a decrease of 50%. (You could also do the sort of thing you did for part a). Then once you find k, you can write the equation they ask for. Hope that helps!
 
Last edited:
TYSM!!! One more thing if you don't mind is that my answers are only right if I didn't include a negative in my original differential equation. I recall my instructor mentioning something about how you shouldn't include a cascading negative but I don't understand why you wouldn't include the negative in an equation about exponential decay.
 
My guess is you accidently got a negative k value?? The way your equations are written, with both of them having the negative sign already built into the equation, you should get a positive k value. If you did get a negative k then the negatives in the differential equation would cancel, which is bad because you're right there should be a negative in that equation. Does that help?
 
Yep that sounds right, I never realized that my initial k value was negative, silly me. Tysm for all the help!
 
You must log in or register to reply here.
Top