Question

Hi, can someone help me with an Algebra 1 question? I really need the help.

Answer 1

What is it I am only 12 so dont expect much xD

Answer 2

I hope you know Algebra. xD @readergirl12

Answer 3

Iris has been studying an invasive population of snails. This particular snail has no local predators, so the population grows wildly. She has observed that the population follows an exponential rate of growth for fifteen years.

1. Create your own exponential function, f(x), which models the snail population. You will need to identify the principal population of the snails and the rate of growth each year. Explain to Iris how your function shows the principal population and the rate of growth, in complete sentences.

Answer 4

Um

Answer 5

Which algebra is this...1?

Answer 6

The course is 'Algebra 1'.

Answer 7

@readergirl12

Answer 8

K Imma have to get my dad So you can the answer Are you okay with waiting?

Answer 9

@trenafuoco

Answer 10

Yeah.

Answer 11

@readergirl12 Just make it quick though and thank you.

Answer 12

Matter of fact I can get some one else

Answer 13

@ganshie8

Answer 14

Fail xD

Answer 15

Haha xD

Answer 16

@iGreen

Answer 17

@aaronq

Answer 18

I hope they are all online.

Answer 19

@tinybookworm

Answer 20

They are supposed to be good at math..I dont wanna get you the wrong answer cause i dont know it

Answer 21

Its okay; is your Dad around or no?

Answer 22

He's looking in his book but thanks gonna take too long

Answer 23

Thats

Answer 24

Oh.

Answer 25

www.purplemath.com/modules/expofcns.htm

Answer 26

Hmmm... I don't understand this.

Answer 27

Me either xc

Answer 28

Do you know what a exponential function is?

Answer 29

www.mathsisfun.com/sets/function-exponential.html

Answer 30

Uhm I have an idea but it may be wrong.

Answer 31

What is it?

Answer 32

Please tell the idea you have. I've been stuck on it for a while. @tinybookworm

Answer 33

@readergirl12 I do know what it is. its f(x)=a^x

Answer 34

Let say the population of snails is P.

Answer 35

Okay.

Answer 36

Then the rate of growth is r.

Answer 37

Then x is the numbers of years. G and r are constant. x is the variable

Answer 38

We will have the function \(y = G.r^x\)

Answer 39

Yeah. I kinda see where you are going with this.

Answer 40

Sorry I mean \(P\) instead of \(G\).

Answer 41

Okay. :)

Answer 42

For example, the original population is 1000. And the rate of growth is 1.5

Answer 43

So the population will be \(1000 \times 1.5=1500\) after the first year.

Answer 44

Okay. :)

Answer 45

After the second year, the population will be \(1500\times 1.5 =1000\times 1.5^2=2250\)

Answer 46

Okay, is that it for this question? I have three more that needs to be answered.

Answer 47

Okay. I will do my best to help you

Answer 48

Did you get it right?

Answer 49

@readergirl12 Yeah. :)

Answer 50

YAY WE DID IT

Answer 51

2. A local snail population grows according to the function g(x) = 200(1.03)2x. Demonstrate the steps to convert g(x) into an equivalent function with only x as the exponent. Then, explain to Iris how the key features of this local snail population compares to the key features of the invasive population.

Answer 52

Yeah, and there is two more after this one.

Answer 53

Is \(g(x)=200(1.03)^{2x}\)?

Answer 54

Yes.

Answer 55

As you know, \((1.03)^{2x}\) can be written as \((1.03^x)^2\) or \((1.03^2)^x\). Can you see how to write the function with only x as the exponent?

Answer 56

Yes. :)

Answer 57

\((1.03^2)^x=1.0609^x\). So the function can also be written as \(g(x)= 200\times 1.0609^x\)

Answer 58

Thank you, is that it for this question?

Answer 59

@tinybookworm

Answer 60

Sorry. I can't solve the second part: "Then, explain to Iris how the key features of this local snail population compares to the key features of the invasive population."

Answer 61

Oh Okay, thats fine. I can figure that part out. @tinybookworm

Answer 62

Let me post the third question.

Answer 63

3. Iris wants to graph the invasive snail population to show the city council. Justify what the appropriate domain and range would be for the function f(x), what the y-intercept would be, and if the function is increasing or decreasing.

Answer 64

I think the domain will be \([0,+\infty\)) and the range will be \([P,+\infty)\), with \(P\) is the original population

Answer 65

Okay. :) And that will be it for this question?

Answer 66

Oh, the y-intercept will be (0,P) and the function is increasing

Answer 67

Okay :) Now for the fourth question.

Answer 68

4. In five years, a garden festival plans on using the park where Iris has been studying the invasive snails. Explain to the garden festival committee how to find the average rate of change for the snail population between years 2 and 5. Describe what this average rate of change represents. @tinybookworm

Answer 69

I think to find the average change, we can calculate the difference in population between year 5 and year 2, then divide by 3

Answer 70

You mean the totals from years 2 and 5 that we had earlier? Subtract them, and divide by 3?

Answer 71

Yes I think

Answer 72

Okay. Is it that it on that problem?

Answer 73

Sorry. But I don't know what the rate of change represents.

Answer 74

Its fine. I'll figure it out. Oh crap I forgot, there is three more questions. Are gonna still stick around for a bit longer for more questions? :) @tinybookworm

Answer 75

Sure

Answer 76

Alright, give me a moment.

Answer 77

2. Create an exponential growth function, f(x), to model a population of frogs that is growing every year. Identify the principal amount, the growth rate, and the appropriate domain and range for your function. Explain how these key features would affect the graph of f(x).

Answer 78

I think the function will be \(f(x)=P.r^x\) too. Same domain, \([0,+\infty)\), and range, \([P,+\infty)\).

Answer 79

Okay. is that it for this question?

Answer 80

I think we can explain these like what we did to the first problem

Answer 81

Okay. Lets move on to the next question.

Answer 82

Using your function f(x) from question 2, demonstrate and explain how to find the average rate of change between year 3 and 5, and between year 5 and 7. Explain what the average rate of change represents to the frog population.

Answer 83

Same way. Subtract the population in year 5 by the population in year 3 and then divide by 2

Answer 84

Okay, thank you! :D

Answer 85

You are very welcome