Question

PLEASE HELP!
In a certain memory experiment the rate at which a student of German memorizes words is given by M'(t)=0.2t-0.0004t^3 where M(t) is the number of German words memorized after t minutes.

Find M(t), if M(0)=0

Answer 1

I got \[\int\limits_{}^{}0.2t-0.0004t ^{3}
= 0.1t ^{2}-0.0001t ^{4}\]

M(0)= \[0.1 (0)^{2}-0.0001(0)^{4}\]

=0?

I think it's wrong

Answer 2

when you integrate you also get a term that represents a constant

Answer 3

so:\[\int\limits_{}^{}0.2t-0.0004t ^{3}
= 0.1t ^{2}-0.0001t ^{4}+C\]where C is some constant - usually determined by the initial conditions.

Answer 4

so, using the initial conditions given to you, you should get:\[M(0)=C=0\]therefore C=0. Therefore:\[M(t)=0.1t ^{2}-0.0001t ^{4}\]

Answer 5

Oh yes, I forgot the +C Ok so I don't substitute the M(0) for t, I substitute it for C?

Answer 6

you use the fact that M(t) = 0 at t=0 to calculate the value of C - which, in this case, turns out to be zero

Answer 7

just to clarify - the integral gave you:\[M(t)=0.1t ^{2}-0.0001t ^{4}+C\]we then use the fact that M(t)=0 at t=0 to get:\[0=0.1*0^2-0.0001*0^4+C=C\]therefore:\[C=0\]therefore:\[M(t)=0.1t ^{2}-0.0001t ^{4}\]

Answer 8

ahhhhhh yes! That actually makes sense!!! Thank you!!

Answer 9

yw :)