ODE question part 2Watch

#1
can someone please check if this is right? thanks

Q. a new company is being formed. A market analysis predicts that the rate of growth of the company's income at any future timme t will be proportional to the difference between the actual income at that time and an upper limit of $10 million. It is also estimated that the income after 4 years will be$4 million. The income is \$0 initially. Find and expression for the income at time t.
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working:

, now plugging in I=0 when t=0

how do i find k?
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9 years ago
#2
it is also estimated that the income after 4 years will be 4 million.
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#3
yes but what formula do i plug the values in, 3rd line of working?
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9 years ago
#4
(Original post by Chewwy)
it is also estimated that the income after 4 years will be 4 million.
PC you should consider substituting this to find k.
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#5
yes, i know but in which equation, thats my problem, is it in as i know c, t and I? or is it another one, please tell me
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9 years ago
#6
(Original post by Prokaryotic_crap)
yes, i know but in which equation, thats my problem, is it in as i know c, t and I? or is it another one, please tell me
That would seem reasonable
You should also, consider, what would happen if you substituted a line after, and ask why you still get the same answer. (my point is either line is fine)
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9 years ago
#7
(Original post by Prokaryotic_crap)
yes, i know but in which equation, thats my problem, is it in as i know c, t and I? or is it another one, please tell me
Any - the equations will give k regardless which one you use.
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#8
so plugiing ...

k=0.023, something is wrong
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#9
Finally!

im pretty confident that, i done it by plugging the value and also done it by using logs and the same value came up. Here is my first method:

, plugging t=4 and I=4x10^6

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9 years ago
#10
(Original post by Prokaryotic_crap)
Finally!

im pretty confident that
Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse.
k=\frac{ln(1^6}{4)
, i done it by plugging the value and also done it by using logs and the same value came up. Here is my first method:

, plugging t=4 and I=4x10^6

Check you valu for when you take way I and note that the log(1) = 0 always so k is not the same value.
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#11
, corrected now
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#12
right?
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#13
yep, pretty confident
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