Question

Algebra ll Help..Medal,Fan...

Answer 1

@ganeshie8 hi can you help
Both 4 and 5

Answer 2

@Kainui

Answer 3

@mathmate

Answer 4

here's what i know so far:
we know that the number of visitors increase exponentially as the temperature increase and linear represent the people who leave the zoo so if we subtract both equations/functions from each other we would get the number of people at the zoo at a specific temperature

Answer 5

Thank you @NvidiaIntely

Answer 6

@mathmale

Answer 7

GG

Answer 8

You'll need to come up with models that reflect what's happening here.

Let n represent the number of visitors. n depends exponentially on the temperature, T, so
n=f(T) = ke^T (which is an exponential function).

Let L(T) represent the number of people who leave the park early. This is NOT the same as n(t), the number of park visitors. Function L(t) is linear, and thus its form must be
L(T)=mT. This states that if the temperature increases, the number of people, L, leaving the park early is a constant times the temperature, T.

Think these thru. Do they make sense to you? If not, explain why. Questions?

Answer 9

Yeah looks terrific
we can subtract the number of people leaving the zoo from the number of people entering the zoo to get the total amount of people in the zoo at a specific temperature. So lets say the exponential part of the attendance can be modeled by the following
\[f(t)=a*b^(t−h)+k\] t - h is the power.
Then we have to subtract the linear part g(t)=mt+c

because we are losing attendance. So the final result would be:
P(t)=(a⋅b^(t−h)+k)−(mt+c)
where P stands for population in the zoo at temperature t.

is that correct? am i missing anything?

Answer 10

for the question 5 i wrote this
we can find the inverse of an exponential function by following the steps below:
1- we have to change f(x) into y
2- we have to switch the x and y variables.
3- we have to solve for y
4- after solving for y name it f^-1(x)

After finding the inverse function we have to substitute x = 250 to find the needed value.

Is that enough

Answer 11

Assuming that these two models are correct (which is not a given), we are to look for a way to combine these two equations into one. One way of doing that would be to eliminate the variable T.

That requires that we solve one or the other equation for T.
I would start with n=f(T) = ke^T. Applying the ln operator to both sides of this equation results in ln n = ln k + T, which is similar to your result.

Answer 12

I'd then substitute ln n-ln k = T for T in the other equation.

Answer 13

just like solving systems of equation? interesting. so mine was wrong?

Answer 14

I agree that we could interpret P as the net number of park visitors. But I eventually solved for temperature, T, so your result and mine differ: yours has tempoerature T, whereas mine does not.

How do we resolve this conflict?

Answer 15

Looks like you've moved on to Question 5, whereas I'm still on Question 4.
One at a time, please. ;)

Answer 16

okay well you tell me :) and sorry for moving to Q5

Answer 17

We've been discussing four variables: T, P, n and L. We'll have to eliminate 2 of those to obtain a function with one dependent variable and one independent variable. Have you thought of this?

Answer 18

You have introduced the function f, which means we have 5 variables floating around in the swimming pool. Again, we've got to cut the number of variables via elimiination. Which ones would you personally choose to eliminate, and why?

Answer 19

so to make this clear lets type in the functions we have already

Answer 20

I doubt that there's just one unique "answer" to Question 4. We have the prerogative of eliminating whichever variable or variables we choose, to obtain a function representing whatever we choose it to represent. You mentioned "net number of visitors in attendance," which I believe is an achievable goal.

Answer 21

Please review our discussion. Copy and paste each function you recognize. Then we can analyze what we have.

Answer 22

\[f(T) = ke^T\]
\[L(t) = mt\]

Answer 23

If we let P represent the number of visitors in attendance, and if we let T represent temperature, which component functions would make up the function P(T)?

Answer 24

How would we define P(T) using the other functions we've derived or identified?

Answer 25

Regarding your\[n=f(T) = ke^T\]

Answer 26

and your \[L(t) = mt:\]

Answer 27

aren't we suppose to have 2 functions? 1 exponential and the other linear? This is getting confusing we had 3 now

Answer 28

Please describe what each represents and make sure you and I are using the same variable to represent the same thing. For example, I used n(T) to repr. the number of visitors in attenance, whereas it seems you've used f(T).

Please develop the function P(T), which represents the net number of visitors as a function of time, T.

Answer 29

So this would be a linear function correct? P(t) = st
where p(t) is number of people who leave at certain t temperature

Answer 30

Please define any new variables or constants you use (such as "s"), and please stick with my L(T) to represent the number of people leaving at temperature T. Adding new vars or consts. complicates the issue, doesn't it?

Answer 31

okay so L(t) = st
s would be the slope which is also the change

Answer 32

is that correct?

Answer 33

Not so much correct as acceptable; my function for the same purpose was L(T)=mT. There is no advantage here to substituting t for T or s for m.

It's your homework, so please choose one version of this function and totally eliminate the other one, for the sake of simplicity.

Answer 34

Lol, So are we set to L(T) = mT? Now what do i do
am as confused as you are

Answer 35

we have to set the exponential function now correct?>

Answer 36

and then ?

Answer 37

i know teaching can be awful lol bare w me

Answer 38

I'm not confused, Will, I'm just asking you not to introduce new constants and variables unless you simultaneously get rid of the old ones permanently.

Again, it seems that our goal is to develop a function P(T) that represents the NET number of visitors at the park as a function of temperature T (not t).

It seems to me, then, that this function would look like P(T_= mT + (exponential part).

You give that a stab, please.

Answer 39

Review our entire discussion. Haven't we already come up with a function representing the exponential part?

Answer 40

we have this is the one
f(T)=ke^T

Answer 41

to get this clear and walk step by step T is temperature and k is?

Answer 42

k is a constant coefficient, just as m is a constant coeff in L(T)=mT. You weren't asked to find k, but should insert it as a placeholder.

Answer 43

great. Now what you want me to do? Do we subtract the exponential function from the linear?

Answer 44

I mean, should insert the constant coeff as just "k"

Answer 45

Let me play the devil's advocate. Why would you subtract?

Answer 46

We're talking about what Will wants to and has to do, not about what mathmale wants Will to do. ;)

Answer 47

Amazing question! Because if we subtract them from each other we would get the number of people at the Zoo at a certain temperature T
Lol and MathMale i love you you're the best

Answer 48

Thank you. Love you too, for your persistence and obvious good preparation.
Exactly. if you subtract the expo. comp. from the linear comp., you'll have a formula for the net number of zoo visitors. Excellent.

Answer 49

Fabulous!
So now ke^T - mT

So the new function we can name it as S(T) = ke^T - mT
i don't think we can somplify any further can we?

Answer 50

@mathmale you not leaving me are you? Leaving a man behind is a sin lol

Answer 51

A sin? I repent. I also bow at your feet and thank you from the depths of my heart for the lovely testimonial.

Answer 52

and repent again.

Answer 53

Lool i love you 2x now

Answer 54

don't solve for x lol

Answer 55

One way to double check on the correctness of your result would be to test it to ensure that the result is positive. We wouldn't want to end up with a net of -247 visitors, would we? Or are we living on a different planet than the rank and file?

Answer 56

I'll rewrite that in terms of z and solve for z, with your leave, of course.

Answer 57

I'm not saying your answer is wrong! I'm just urging you to check that its range is positive, not zero or negative.

Answer 58

Yeah i hear you well. So The answer was
S(T) = ke^T - mT
if we have the Temp = 86
you said k is constant so can it be 6? and m is also constant so 4 and what about e?

Answer 59

I'm grieving for that poor P we were discussing. Seems as tho' you've abandoned it in favor of S(T). How sad.

We have several different unknown constants and one unknown variable here, so it may not be realistic for you to try to obtain a specific S(T) value. I'd suggest you can safely rest on your laurels now that you've gotten a new function based upon the given data, even if you don't have spec. values for the constants.

Answer 60

Mind moving on to #5?

Answer 61

Sure let's role

Answer 62

Role? Am I your role model, or your roll model, neither or both?

Answer 63

Lol am a model you're my math model <3

Answer 64

I'm fat, so if you were to roll me out, the remains of me would be very wide.

Answer 65

Loool Just like the exponential growth? a math joke lol math jokes seem funny

Answer 66

On the other hand, if I'm your role model, then my head (alone) might expand a bit much.

Answer 67

i wouldn't wonder! you have many info in that head so it has to expend lol

Answer 68

Your prerog.: choose a variable to represent the number of pairs of jeans this guy owns.
I promise not to toss it out and replace it with another variable that I like better.

Answer 69

Lool
13?

Answer 70

No variable omg S

Answer 71

wait i can see why you choose the variable M everytime.. MathMale double M ... hmm

Answer 72

Actually, our friend Lon has already come up with a name: It's f (also written as f(t).
So neither 13 nor omg S apply here. ;(

Answer 73

(review question #5)

Answer 74

So f(t) represents the number of jeans that our other friend, Tim, owns, as a function of time.

Answer 75

right so f(x) and it is exponential function and they want the inverse

Answer 76

(who cares?)

Answer 77

Let's mock up f(t) first. Agreed: f(t) is an expo fn. So, what would your model look like?

Answer 78

Lol okay so if we have function f(t) i would 1st change the name f(t) to y because that name kinda ugly

Answer 79

Your indept. var. must be t (representing time). There must be a constant of proportionality. OK, so long as you take notes reminding yourself that the original function name was f. Sure, the first step to finding the inverse of a function f(t) is to replace f(t) with 'y.' Way to go, man.

Answer 80

So, let's see your proposed model for f(t).

It's an expo function, remember?

Answer 81

yeah

Answer 82

So...

Answer 83

you want me to say the 2nd step or ?

Answer 84

Nope. i want you to come up with an appropriate model for an expo. growth function.

Answer 85

okay leave that to me Mr

Answer 86

You don't yet have a function, so it's too early to try to find the inverse
.
Mr. Goldmann.

Answer 87

So, your lovely creation is the function f(t) = ?????? which is an expo function

Answer 88

wait why don't you handle that Lool ..
So do you want the function in the exponential form like p* 1 + r)^x or ab^x? you pick

Answer 89

Nope, I asked you first, so you're stuckw ith the task. You did fine in the previous question...you knew how to develop a model for expo grth.

Answer 90

I pick? Why me?

Answer 91

okay
f(t) = 2^t

Answer 92

the first possibility you listed has connections to compound interest and other applications.
No you won't.
Question: Why have you chosen the base 2 for your expo function?

Answer 93

it can't be 1 because then it will be linear and 2 is growth so why not

Answer 94

Uhm silence makes me question my whole math skills lol

Answer 95

2 would work, actually. But why 2?
From our previous problem (#4), n=f(T) = ke^T

There we used the base e, which is one of the most commonly used bases, most general, and applicable here.

Answer 96

No reason for you to question your whole set of math skills! You're doing fine, actually.
Give and take is important. Want this to be both instructive and fun for you.

Answer 97

yeah absolutely i love learning so tell me the reason of 2