Question

The number N of employees at the Ajex Steel Company is growing at a rate given by the equation N'(t) = 20e^(.01t) where N is the number of people employed at time t, in years. The number of employees currently is 400. Find an equation for N(t).

Answer 1

If no one else posts a solution I will. Give me a minute

Answer 2

oh thank u

Answer 3

umm i have the solution i just dont know how to set it up

Answer 4

I understand

Answer 5

1. To find N(t), take the integral of N'(t):
\[N(t) = \int\limits{ 20e^{.01t} dt}\]2. Remove the constant, 20, from the integral: \[20 \int\limits\limits{ e^{.01t} dt}\]3. Let u = .01t Then du = .01dt and: \[dt = \frac{du}{.01}\]4. Next substitute everything in terms of u and du: \[20 \int\limits\limits\limits{ e^{u} \frac{du}{.01}}\]5. Move the constant 1/.01 outside of the integal: \[\frac{20}{.01} \int\limits\limits\limits\limits{ e^{u} du}\]

Can you finish the rest from here?

Answer 6

yes thank you

Answer 7

Don't forget to add plus C after taking the integral!

Answer 8

oh yes

Answer 9

\[20*\frac{1}{0.01} \int\limits e^{0.01t} dt\]

Answer 10

ok i got the part N(t) = 2000e^(.01t) + C but the solution says its N(t)=2000e^(.01t) - 1600? what am i doing wrong?

Answer 11

did you find the constant yet?

Answer 12

Yup that's what has to be found

Answer 13

how do you do that?

Answer 14

400 = 2000^(0.01t) + C i think..

Answer 15

wait..what's the point of me being here since hero know's how to do it :/

Answer 16

Hero, i think that there is something wrong..

Answer 17

Nothing is wrong. If it was, the first part would have been incorrect. The constant is what needs to be found.

Answer 18

okay, im out; since you know how to do it..

Answer 19

Thanks for your contribution @Mimi_x3 . Of course it actually looks like you're bailing out on us but that's okay.

Answer 20

lol

Answer 21

it's 1am for godsakes..
to find the constant..
400 = 2000e^(0.01t) + C

Answer 22

400 = 2000e^(0.01*0) + C
C = -16000
therefore; 2000e^(0.01t) -16000
Done!

Answer 23

-1600*

Answer 24

happy now?

Answer 25

Go to bed now :P

Answer 26

lol thanks

Answer 27

wait..you did not know how to do this hero?

Answer 28

I did actually.

Answer 29

idk who to give the medal to

Answer 30

oh gawd..waster my time arghh

Answer 31

lol

Answer 32

give it to hero..i dont need it

Answer 33

@myluv4u , I already gave @Mimi_x3 a medal, but I am the one who helped you initially.

Answer 34

well thank you both for the help

Answer 35

thank you hero i had already gave you the medal , i forgot