onegirl
A person scores f(x) = 90/1 + 4e^-0.4t points on a test after t hours of studying. What does the person score without studying at all? Compute f’(0) and estimate how many points 1 hours of studying will add to the score.
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onegirl
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This is what I did but my teacher said it was wrong she said ( Find f' and f'(0).)
F(x) = 90/ 1 + 4e^-0.4t
F(0) = 90/ 1 + 4e^-0.4(0) = 18
F(1) = 90/1 + 4e^-0.4(1) = 24.45
So comparing the scote at f(1) and f(0) where at f(1) studying for 1 hour and f(0) studying none.
F(1) - f(0)/24.45 – 18 = 6.45 points
EulersEquation
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Should this have parenteses or not?
Is this F(x) = 90/ (1 + 4e^-0.4t )?
onegirl
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yes prenthesis
onegirl
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like this \[\frac{ 9 }{ 1 + 4e ^{-0.4t}}\]
EulersEquation
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Your teacher specifically said to differentiate?
onegirl
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yes
onegirl
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she said to Find f' and f'(0)
onegirl
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@EulersEquation so do you know how?
onegirl
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@Numb3r1 can u help?
EulersEquation
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Yes. I need to review this. First glance is to use the quotient rule. Do you know how to use the quotient rule? Someone else may want to take a look. I am in the middle of helping someone else. When I finish I'll get on it.
onegirl
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ok
EulersEquation
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Ha! I am terrible at arithmetic. On first run I get a negative number for f'(0). You cannot make a negative score on a test! Unless the teacher doesn't like you.
I am rusty on this. I'll work on it some more. In the meantime, bump the problem and hopefully someone else will tackle this.
onegirl
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okay
onegirl
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@waterineyes
waterineyes
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Just want to take derivative of that??
onegirl
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yes Find f' and f'(0)
waterineyes
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It will come out to be negative..
onegirl
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what will come out? so what i did above is wrong or?
waterineyes
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Wait, let we do it first..
waterineyes
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\[\frac{ 90 }{ 1 + 4e ^{-0.4t}} = \frac{ -(90)(-1.6 \cdot e^{-0.4t}) }{ (1 + 4e ^{-0.4t})^2}\]
waterineyes
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It will become positive now.. :)
onegirl
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okay
EulersEquation
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Yeah. I don't see why it has to be differentiated -- not according to the question.
waterineyes
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Am I right in this?
EulersEquation
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Ah! I forgot to square the denominator!
EulersEquation
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That looks good.
onegirl
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okay thanks!
waterineyes
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So you can now find f'(0) by putting 0 as value of t..
onegirl
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okay
waterineyes
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@onegirl can you go for that?
onegirl
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just plug in 0 and solve right?
waterineyes
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Yep, just simple calculations with calculator..
onegirl
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okay yes i can
waterineyes
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Good..
Keep it up..
onegirl
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i got 0 after i solved