Question

A bank account earns 5% annual interest compounded continuously.

A) assuming that money is continuously withdrawn from the account at a rate of 11000 per year, write a differential equation describing the balance (b) in dollars, in the account (where b is a function of t, measured in years)

B)assuming that money is conitnously deposited into the account at a rate of 11000 per year, write a differntial equation describing the balance B (in dollars) in account ( where B is a function of t, measured in years)

Answer 1

been stuck on this all week
thank you i assume we take deverivate for one and anti dervative for other

Answer 2

but not sure? Thanks for helping out!

Answer 3

I'm having the same problem with one I posted hours ago...
B'(t)= rate of continuous compounding
\[f(b)=11000e ^{0.05b}\]
\[^{} \int\limits_{0}^{n} B\prime(t)(e ^{-0.05t})dt\]
so take the derivative of the first part then inegrate the entire thing by parts?
\[\int\limits_{0}^{t}[(11000e ^{0.05t})\prime (e ^{-0.05t})]dt\]

Answer 4

wait I think the variables are wrong but instead of t use b?

Answer 5

balance due to continuous compounding:
\[b(t)=Pe^{0.05t}\]
but principal = previous year "b"-11000

Answer 6

what do you mean?

Answer 7

\[b(t)=\left[b(t-1)-11000\right]e^{0.05t}\]

Answer 8

?so the other would look like [b(t-1)+11000]e^(.05t)

Answer 9

and this means b is a function of t as well?

Answer 10

it is given that "b" is a function of "t"

Answer 11

does the question say "differential" equation or "difference" equation??

Answer 12

so this work is on iterguals and anti dervitaives so this wouldnt even show up ? i guess thats what confused me

Answer 13

no. no integration

Answer 14

write a diferential equation describing balance B (in dollars) in the account (where B is a function t, measured in years)

Answer 15

so for part A it asked
Assuming that money is continuously WITHDRAWN from the account at a rate of $11000 per year, write a DIFFERENTIAL equation describing the Balance B( in dollars) in the account where B is a function of t, measured in years)

Answer 16

and the next part 2 would be Deposited instead of withdawn

Answer 17

@ electrokid why not? it's over an period of time. Just trying to understand so I can understand my prob w/ CAPITAL VALUE I posted hours ago

Answer 18

so now that i confirmed it is a Differential equation does that change the results?

Answer 19

differential means, in derivative form
defference means -> in the above b(t-k) form..

Answer 20

@TARAMAYO I did not see your previous post. this problem, does not require integration

Answer 21

yea so its DIFFERENTIAL so what would the new equation be then?
and how would i solve it with a withdraw or an deposit?

Answer 22

so how would the new formula look for my equation?

Answer 23

so confusing I hate word probs, why wouldn't a negative rate suffice? as it wud in an equation for the rate of decay?

Answer 24

\[{d\over dt}b(t)=0.05b(0)-11000\\
b'(t)=0.05b(0)-11000
\]
b(0) = balance at t=0

Answer 25

if money is continuously added, you make +11000

Answer 26

rate is always positive since the interest is always added :)

Answer 27

follow people?

Answer 28

im kinda following?

Answer 29

so what would we do if we had money being withdrawn?

Answer 30

the above equation was for "withdrawal"
if money is added yearly, you make it +11000 instead of -11000

Answer 31

shouldnt the .05 be negative?
because lets say I have 100,000 taken out each year wouldnt i lose money if i always took out 11000?

Answer 32

if my rate of change is withdrawling 11000?

Answer 33

no.. the interest rate is always positive.. has nothing to do with withdrawal
interest amount is always added!!!

Answer 34

haha okay cool , just weird not taking the anti derivative

Answer 35

to find the composite function b(t), you take the anti derivative..
but that is not what the question is asking for!!

Answer 36

it wants to know what B'=

Answer 37

but not B(t) just B'=? for withdrawn and deposited

Answer 38

since we have 0.05b(0)−11000
wouldnt that just be -11000 or +11000 because .05(b(0))

Answer 39

where do we put the b at since it says the variable b is not defined?

Answer 40

it just wants to know what B'=?

Answer 41

correct, just the b'(t), and not b(t)

Answer 42

??

Answer 43

so the answer is just -11000 and +11000?

Answer 44

Pe^rt

Answer 45

WHAT!!no
your answer would mean that there is no "continuous compounding at all1!!!!!"

Answer 46

ahhahah HELP ME!!! lol

Answer 47

lol so how would i write this bad boy out?

Answer 48

what was the balance at t=0?

Answer 49

0.05b(0)−11000? it wants a function of B'=?

Answer 50

no,
it wants THE funtion b'(t)

Answer 51

ill send the original equation!!!!

Answer 52

let me upload it real fast!

Answer 53

@dmariscal hurry up. Its 2:30am

Answer 54

i'm not making this up electrokid, this is the formula sheet I got from my instructor (last formula) -- negative rate. I'm not pretending I know what I'm doing but I dont understand either.

Answer 55

okay!!!

Answer 56

okay this is the question and the first part that is covered is the same as part 2 just wants the amount when it is withdrawn

Answer 57

this should be clear now Thanks SO MUCH!

Answer 58

@TARAMAYO its opposite :)
the formula is to find "present" from future...

we are finding future/present from past

Answer 59

???

Answer 60

ohh thats for him!!! What about mine!!! i sent a screen shot!! so its more clear!!

Answer 61

@dmariscal you are in a test. and I have given enough information already, unknowlingly. this is against the code of conduct of the website and unethical. good luck.

Answer 62

the time expired

Answer 63

if you saw this was a screen shot form earlier today at noon

Answer 64

i just wanted to see how to solve it, i already failed the test

Answer 65

isee. :)
ok

Answer 66

@ dmariscal are you taking business calc? when do you have to get this prob done? Holy smokes I just read electrokid's response

Answer 67

so, yes. what we did was right.

Answer 68

how did we put it into terms of B(t) so t would be in our awnser?

Answer 69

@TARAMAYO to be able to use the "@" tool correctly, you should not put a "space" after that "@" symbol.

Answer 70

@electrokid so can you tell me what's my R(t) here? I've been waiting for hours, but if it's too late I'm going to the tutoring center tomorrow. Thanks..
CAPITAL VALUE: Suppose income from an investment starts (at time 0) at $6,000 a year & increases linearly & continuously at a rate of $200 a year. Find the Capital Value at an interest rate of 5% compounded continuously.
Improper integral using R(t)e^(-rt)... Which amount is the R(t)? & what makes the other amount in this problem?

Answer 71

@dmariscal then instead of b(0), put b(t)
:)
\[{\rm withdrawal:}\;B'(t)=0.05B(t)-11000\\
{\rm deposit:}\;B'(t)=0.05B(t)+11000
\]

Answer 72

@TARAMAYO I am looking at it now..

Answer 73

@electrokid you know what, nevermind, it's really late I've got to get up in 3hrs for work

Answer 74

@TARAMAYO so, your rate is, +200 a year

Answer 75

@electrokid Hey super thanks, I appreciate it! gnite!

Answer 76

thanks
so much

Answer 77

one last question
wouldnt it be
.06t+11000

Answer 78

then, its a linear increase.. so,
\[
CV=\int I'(t)e^{-rt}dt=\int 6000e^{-0.05t}dt
\]

Answer 79

the intrest + the intial
?
so why would B(t) be in there

Answer 80

@dmariscal coz, you get some compound interest on whatever the balance you had at time t.. i.e., a lilttle compount intertest of 0.05B(t)

Answer 81

okay cool!!

Answer 82

Thanks again i wish i could pay you on this sight!!

Answer 83

haha.
np.
☮

Answer 84

@dmariscal didn't see you on yesterday so here it is