# Couple Simple Grade 12 Calculas Homework Help NEEDED

1. Apr 4, 2012

### livestrong136

TO EVERYBODY, THIS IS NOT MY HOMEWORK. I HAVE A TEST TOM and these are some questions that I just dont know how to do, I gave attempts to some and some I am just missing something. Plus, these questions are from all over the unit so its not my homework. I need it done asap. So then I know how someone did it and I can understand that way as fast as possible. Thank-you. ALSO SOME OF THEM I MANAGED TO WRITE WHAT I GOT BUT SOME DERIVATIVES QUESTIONS WERE TOO COMPLICATED TO TYPE.

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1. Find the derivative of the following functions using the f(x+h) - f(x)/h

a. ƒ(x) = 1/2x Show all your steps

It did it but I am not getting the right answer.

Just remember its not (1/2)x. It should be 1/(2x)

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2. A rocket is fired into the air with an initial velocity of 98 m/s. The height ( h ) of the rocket after t seconds is given by the expression h = 98t - 4.9t2.
a. What the average rate of change for the first 2 seconds.

Time Height
0 0
1 93.1
2 176.1

Average rate of change = 88.2 m

I know the answer is 88.2. But can anyone please show me the steps thnx.
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3. If you invest \$5000 compounded continuously at 4% p.a. how much will this investment be worth in 5 years?

you should use the formula A(t) = Pe^(rt)

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4. A population of 500 E. coli bacteria doubles every 15 minutes. Use this information to find an expression for this population growth. Using this expression, find what the population would be in 87 minutes. Use an exponential model.

In P(t) = 500 e^kt
for minutes, then:

1000 = 500 e^15k
2 = e^15k
15k = ln2
k = (ln2)/15

Now, I am stuck.
Now, can someone use the formula A(t) = Poe^(kt), and sub in what you know and sub in 87 for t to find A(t).

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5. c. What is the equation for the derivative of y = (0.75)x?

I GOT THIS y = 1.00000022063(0.75)x
I have 1.000(0.75)^x as an answer, but the 1.000.... is incorrect.. CAN SOMEONE FIX IT.

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6. Find the derivative of the following functions using the f(x+h) - f(x)/h Show all your steps

a. ƒ(x) = x^2 + 5x

b. ƒ(x)= 1/2^x

Last edited: Apr 4, 2012
2. Apr 4, 2012

### micromass

Staff Emeritus
Please provide attempts to ALL the questions, or this will be deleted.

3. Apr 4, 2012

### livestrong136

Well some of them I dont know where to begin. SO that means I CANT GET HELP HERE IF I DONT KNOW WHERE TO START. plus, these are only 6 questions and some of them I have written down by answer and some of them i am half done. But some I just dont know where to begin so that means I cant get help??? :(

4. Apr 4, 2012

### livestrong136

Can you just answer these please, I'll learn from the answers, these are these only six I am stuck on, if I get these, then I am good.

5. Apr 4, 2012

### micromass

Staff Emeritus
1 and 6. Plug in everything in (f(x+h)-f(x))/h

2. What is the elevant formula for average rate of change?

3 and 4. What is P, r and t?

5. You have something of the form y=ax for a constant. What is the relevant formula?

6. Apr 4, 2012

### micromass

Staff Emeritus
No. This is not how this forum works. Do not ask again.

7. Apr 4, 2012

### livestrong136

OK so if I don't know where to start that means I cant ask for help????

8. Apr 4, 2012

### micromass

Staff Emeritus
I gave you hints/suggestions in post 5.

9. Apr 4, 2012

### livestrong136

FOR # 4

P= 5000
i= .04/365 = .0001096
n=1025

5000 (1.0001096)^1025
= 5594.43

I asked my teacher too she said my answer is only like 500 away plus she told me to use the formula A(t) = Poe^(kt), and sub in what you know and sub in 87 for t to find A(t).

10. Apr 4, 2012

### micromass

Staff Emeritus
I don't know the name of your variables.

Try it this way:

After 0 minutes, there are 500 bacteria.
After 15 minutes, there are 500*2 bacteria
After 15*2 minutes, there are 500*2² bacteria
...
How many bacteria are there after 15n minutes?

11. Apr 4, 2012

### livestrong136

For #1, I dont know how to put in, this is what I did

1/2(x+h) - 1/2(x)
----------------
h

BUT ITS NOT (1/2)x. It should be 1/(2x).. and I dont know how to put in 1/(2x)

12. Apr 4, 2012

### micromass

Staff Emeritus
So you have

$$\frac{\frac{1}{2(x+h)}-\frac{1}{2x}}{h}$$

Try to add up the two fractions in the numerator.

13. Apr 4, 2012

### livestrong136

I got to this point....

(1/2x) + (1/2h) - (1/2x) x (1/h)

14. Apr 4, 2012

### micromass

Staff Emeritus
Nooooooo.

It is NOT true that 1/a + 1/b = 1/(a+b).

Try to add up the fractions using the correct formula. Hows do you add up two fractions?

15. Apr 4, 2012

### livestrong136

I am really confused.

16. Apr 4, 2012

### livestrong136

or you meant...

1/(2x+2h)-1/2x ... wouldnt it be 1/2h left??? so we have 1/2h x 1/h.. we cross multiply, we get h/2h= 1/2

17. Apr 4, 2012

### micromass

Staff Emeritus
No, that is incorrect.
You should review how to add up fractions.

18. Apr 4, 2012

### Ray Vickson

Well, suppose x = 1 and h = 0.1. You want to compute 1/2.2 - 1/2, and you are asking whether this equals 1/0.2. Just compute it and see for yourself.

RGV