Question

Show work & Help me! :D Medal will be rewarded! :D I need help on 57 - 61 on page 529. Help me get started on each problem please! :D Here's the link: http://www.mrlarkins.com/algebra2/docs/chap10.pdf

Answer 1

@dumbcow

Answer 2

So for 57 we'll use an exponential function of the form \(\large y=ab^x\) as was used in example 3 of the champter.

\(\large a\) is our initial amount of bacteria.
Problem 57 tells us are timer starts at 2pm. So that will be our initial time.

There is a little chart to the right, it says at 2pm, we have 100 bacteria.
So that is telling us that our initial amount of bacteria, \(\large a\) equal 100.

\(\large y=100b^x\)

Does that much make sense so far?

Answer 3

chapter* our*.. wow i made some typos in there. lol

Answer 4

It's okay I am sorry about the link

Answer 5

no probs c:

Answer 6

yea it makes sense

Answer 7

\(\large x\) is time
\(\large y\) is bacteria

The chart is also telling us that at 4pm (This is when 2 hours have passed), the bacteria has grown to 4000.

So they're saying when \(\large \color{orangered}{x=2}\) (2 hours passed), that \(\large \color{green}{y=4000}\)

So let's plug these values in, and solve for \(\large b\).

Answer 8

\[\large \color{green}{y}=100b^{\color{orangered}{x}} \qquad \rightarrow \qquad \color{green}{4000}=100b^{\color{orangered}{2}}\]

Answer 9

So you think you can solve for \(\large b\) from that point?

Answer 10

4,000 = 100b^2

Answer 11

We want to get the b value alone.
So maybe start by dividing each side by 100.

Answer 12

I got the answer

Answer 13

y = 100(6.32)^x

Answer 14

Cool, looks good so far.

Answer 15

On 58, I put, "On the table at x = 7 it says 4.03E7 = 40,273,516 million bacteria. Is that the right answer?

Answer 16

Ok realize that they're trying to trick you a little bit here.
We're not dealing with \(\large x=7\).

We're dealing with 7pm, which is 5 hours passed our starting time.

Answer 17

on the table what should I look for

Answer 18

We used the table to get our \(\large a\) value,
and we used the table again and did a little math to get our \(\large b\) value.
We don't need the value anymore.

We've successfully setup our bacteria function, without any missing information, \(\large y=100(6.32)^x\)

Now they want to know how much bacteria \(\large y\) will there be at 7pm, \(\large x=5\)

Answer 19

on the table go to x=5

Answer 20

what table? D:

Answer 21

on my calculator

Answer 22

oh oh oh i see :)

Answer 23

am i right?

Answer 24

If you put the function into your calculator and made a table, then yes, look for x=5 and find out what your y value is.

Answer 25

at x = 5 it says 1.01E6 = 1,008,289.84082

Answer 26

yup looks good.

Answer 27

can I put the numbers: 1,008,289 million bacteria

Answer 28

If you're to round to the `hundredths` place, then we are rounding off to 2 decimals.
So for our answer we would want to put,
y=1,008,289.84

Answer 29

could we leave it as 1,008,289 million bacteria

Answer 30

ya that's probably ok.
make sure you don't put the word million after it like you did.

Our bacteria is amount equal to,
1,008,289

Which we could write as
1.008289 million.

See how we have just over 1 million?
The way you wrote it, it looks like a million millions.

Answer 31

I kind of know how to write an exponential function on #59

Answer 32

I started #59:
y=ab^x
5.31=3.93b^10 <---- but I think it's wrong.

Answer 33

Keep in mind that "an exponential function" is not particularly well-defined.

These are exponential functions:

\(y = Ae^{-bx}\) -- And probably is what is wanted.

\(y = Ab^{x}\) -- Perfectly acceptable

\(y = A + B^{cx}\) -- No one said "Purely" exponential.

\(y = \dfrac{A}{B + Ce^{Dx}}\)

1790 3.93 million
1800 5.31 million

That's all you need.

Choose an appropriate form: \(y = Ae^{b(x-1790)}\)

I decided to index to 1790, choosing 1790 as the base value. This form also gives IMMEDIATELY, A = 3.93.

\(y = 3.93e^{b(x-1790)}\)

All that is left is to use the 1800 data to find "b". Go!

Answer 34

I have 59, I need help on 60 & 61 can you get me started on them, I have to go to bed.

Answer 35

I'm a little troubled by this. If you did 59, there really is no excuse for not getting 60. 59 is the perfect setup for 60. Just enter the values and read off the results!

What model did you get in 59 and what does it mean?

Answer 36

What answer

Answer 37

function

Answer 38

You stated, "I have 59". What did you get? What exponential function did you define to fit those two data points?

Answer 39

y = 3.93(1.35)^x

Answer 40

Okay, what is 'x'? Is that years or decades or what?

Answer 41

I don't know what do you think it is

Answer 42

You designed it. Did you WRITE DOWN a definition? If not, you have nothing.

Answer 43

It says decades

Answer 44

every ten years = 1 decade

Answer 45

1.35 * 3.93 = 5.3055

Okay, it looks like you intended x to be decades since 1790.

Verify

x = 0 IS 1790
3.93*(1.35)^0 = 3.93 * 1 = 3.93

x = 1 corresponds to 1800
3.93*(1.35)^1 = 3.93 * 1.35 = 5.31

Fine. Now just answer all the question in 60

x = 2 corresponds to 1810
3.93*(1.35)^2 = 3.93 * 1.82 = 7.16

Answer 46

Note: x is NOT just "decades". It is "decades since 1790". Please be careful to write a good and complete definition so that you are not confused the next time you look at it.

Answer 47

the answer is right correct

Answer 48

Do you use the answer from 59 to help answer #60

Answer 49

?? What answer? You seem to have a good model for problem 59, if you remember what it is. Problem #60 requires you to explore it's properties for other years. The correct answer is your exploration. Explore!

59 is the model building.
60 is the exploration of that model that you just built.

Answer 50

Explain easy and able to understand, not to be mean or anything.

Answer 51

I refuse to dump answers. I want you to stretch your mind and learn the material. I could just hand things to you, but I do not believe that will be in your best interest.

Part of the study of mathematics is learning what may be a way of thinking that does not come to you naturally. It may be like learning another language. Getting your mind to think in a linear and logical manner may require more exertion than you expect. I intend to encourage that exertion.

Answer 52

right, so what do you mean???

Answer 53

What do I mean about philosophy or about problems #59 and #60?

Answer 54

Past my bedtime. gtg.

Answer 55

59/60