The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

confusing differential question

the value £v of a car t years after the 1st january 2001 is given by the formula v=10000x(1.5)^-t

find the value of dV/dt when t=4

how do you differentiate is, because i understand you need to use the a^x=a^x lna rule but then what do you do with the 10000.
Just factor it out:
ddt[10000f(t)]=10000ddt[f(t)]\frac{d}{dt}[10000f(t)]=10000\frac{d}{dt}[f(t)]
Reply 2
Avatar for Byrney11
Byrney11
OP
Original post by ben-smith
Just factor it out:
ddt[10000f(t)]=10000ddt[f(t)]\frac{d}{dt}[10000f(t)]=10000\frac{d}{dt}[f(t)]


but when i did that i got 10000*(1.5)^-t *ln1.5
whereas the markscheme says you need -10000
(edited 12 years ago)
Lol.
Original post by Byrney11
but when i did that i got 10000*(1.5)^-t *ln2
whereas the markscheme says you need -10000


you are doing it wrong
Reply 5
Avatar for Byrney11
Byrney11
OP
Original post by ben-smith
you are doing it wrong


how does the 10000 turn negative
Reply 6
Avatar for nuodai
nuodai
17
Original post by Byrney11
how does the 10000 turn negative


It doesn't. Your error is thinking that you have something of the form ata^t when in fact you have something of the form a−ta^{-t}. Hint: chain rule.

On a side-note, try to avoid writing things like this:
Original post by Byrney11
a^x=a^x lna

It probably won't go down well in an exam :p:
Original post by Byrney11
how does the 10000 turn negative


laws of logs and exponentials:
v=10000(1.5−1)t⇒v′=10000ln(1.5−1)1.5−t⇒v′=−10000ln(1.5)1.5−tv=10000(1.5^{-1})^t \Rightarrow v'=10000ln(1.5^{-1})1.5^{-t} \Rightarrow v'=-10000ln(1.5)1.5^{-t}
Reply 8
Avatar for Byrney11
Byrney11
OP
oh s*** of course lol cheers pal
Original post by nuodai

On a side-note, try to avoid writing things like this:

It probably won't go down well in an exam :p:


lol, I hadn't seen that. We've all done it though.

Why haven't you updated your blog:angry:, I thought the friday topology thing was awesome:tongue:
Reply 10
Avatar for nuodai
nuodai
17
Original post by ben-smith
lol, I hadn't seen that. We've all done it though.

Why haven't you updated your blog:angry:, I thought the friday topology thing was awesome:tongue:


It's not really a blog, so it doesn't need updating as such :p: And besides the fact that I currently have nothing interesting to waffle about, I have exams at the moment.
Original post by nuodai
It's not really a blog, so it doesn't need updating as such :p: And besides the fact that I currently have nothing interesting to waffle about, I have exams at the moment.


fair enough.

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you