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avatar+1313 

Use seperation of variables to solve for the solution when dQ/dt=Q/5, Q(0)=50. 

1/QdQ=1/5dt

● 1/QdQ=●1/5dt

● 1/QdQ=1/5●dt

lnQ=1/5t + C

e^lnQ=e^1/5t x e^C

e^lnQ=e^1/5t x e^C

Where is my error? 

Answer is Q equals 50e^(1/5)t. I dont have the exponent of (1/5)t. Also why were brackets applied to the fraction?

 Aug 16, 2014

Best Answer 

 #3
avatar+128460 
+13

Let's take it from your third step, Stu

lnQ=1/5t + C

We don't really need to exponentiate both sides...just write this in exponential form....so we have...

e^[(t/5) + C] = Q

Ce^(t/5) = Q

And when t = 0, Q = 50....so C = 50   and we have

Q(t) = 50e^(t/5)

 

 Aug 16, 2014
 #1
avatar+4473 
+13

Brackets were applied to the fraction because it could be read as Q = 50e^1/5t [Note 5t is in the denominator].

 Aug 16, 2014
 #2
avatar+1313 
+8

Oh i was there. Thanks.

 Aug 16, 2014
 #3
avatar+128460 
+13
Best Answer

Let's take it from your third step, Stu

lnQ=1/5t + C

We don't really need to exponentiate both sides...just write this in exponential form....so we have...

e^[(t/5) + C] = Q

Ce^(t/5) = Q

And when t = 0, Q = 50....so C = 50   and we have

Q(t) = 50e^(t/5)

 

CPhill Aug 16, 2014

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