## onegirl 2 years ago 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.

1. onegirl

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

2. EulersEquation

Should this have parenteses or not? Is this F(x) = 90/ (1 + 4e^-0.4t )?

3. onegirl

yes prenthesis

4. onegirl

like this $\frac{ 9 }{ 1 + 4e ^{-0.4t}}$

5. EulersEquation

Your teacher specifically said to differentiate?

6. onegirl

yes

7. onegirl

she said to Find f' and f'(0)

8. onegirl

@EulersEquation so do you know how?

9. onegirl

@Numb3r1 can u help?

10. EulersEquation

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.

11. onegirl

ok

12. EulersEquation

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.

13. onegirl

okay

14. onegirl

@waterineyes

15. waterineyes

Just want to take derivative of that??

16. onegirl

yes Find f' and f'(0)

17. waterineyes

It will come out to be negative..

18. onegirl

what will come out? so what i did above is wrong or?

19. waterineyes

Wait, let we do it first..

20. waterineyes

$\frac{ 90 }{ 1 + 4e ^{-0.4t}} = \frac{ -(90)(-1.6 \cdot e^{-0.4t}) }{ (1 + 4e ^{-0.4t})^2}$

21. waterineyes

It will become positive now.. :)

22. onegirl

okay

23. EulersEquation

Yeah. I don't see why it has to be differentiated -- not according to the question.

24. waterineyes

Am I right in this?

25. EulersEquation

Ah! I forgot to square the denominator!

26. EulersEquation

That looks good.

27. onegirl

okay thanks!

28. waterineyes

So you can now find f'(0) by putting 0 as value of t..

29. onegirl

okay

30. waterineyes

@onegirl can you go for that?

31. onegirl

just plug in 0 and solve right?

32. waterineyes

Yep, just simple calculations with calculator..

33. onegirl

okay yes i can

34. waterineyes

Good.. Keep it up..

35. onegirl

i got 0 after i solved