urgent help needed for physical applications of calculus (1 Viewer)

[johnle95]

hi guys
how would u do the questions attached?

 

[Parvee]

10.
When t=0, N=3000
3000=1800+Ae^0
A=1200
When t=3, N=3400
3400=1800+1200e^3k
1200e^3k=1600
3k=ln(16/12)
k=[ln(16/12)]/3
k=0.09589.....

a) N=1800+1200e^5k
=3738

b) 8000=1800+1200e^kt
6200=1200e^kt
e^kt=6200/1200
kt= ln(6200/1200)
t= [ln(6200/1200)]/k
t=17.13 yrs

 

[Parvee]

8.
a) dv/dt=-kAe^-kt
=-k(P+Ae^-kt +P)
=-k(v-P)

b) 0=500+Ae^0
A=-500

21=500-500e^5k
-479=-500e^5k
e^5k=479/500
5k= ln(479/500)
k= [ln(479/500)]/5
= -8.58x10^-3

c) v=500-500e^20k
= 78.85ms^-1

d) As t --> infinity
e^kt --> 0
Therefore v=500 - 500(0)
v=500ms^-1

 

[Parvee]

I'm not gonna do the rest....
All these questions basically have the same process, so you should be able to do the other ones.

 

[johnle95]

I'm not gonna do the rest....
All these questions basically have the same process, so you should be able to do the other ones.

i just have trouble interpreting the questions
could u please please do the rest?