Question

Am I doing this right?

Answer 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 2

f(x) = a(b)^x

Answer 3

Or is that f(x) = P(b)^x

Answer 4

Well the principle is what you start off with

Answer 5

f(x) = 50(3)^15

Answer 6

Yes, so that means I can choose any random number to start off with? @swagmaster47

LIke in my example, 50.

Answer 7

So that would look like (Population of Snails)(Rate per)^(day)

Answer 8

I would think so, if they didnt provide one for you

Answer 9

@SolomonZelman

Answer 10

I am making it triple (b) which I placed a 3 insider.

Answer 11

Good, but the exponent part is years, not days.

Answer 12

Which test are you taking? @Conqueror

Answer 13

I am not taking any test, why do you want to know?

Answer 14

What do you mean? @SolomonZelman

Answer 15

Nevermind, I remember that question so I was going to see what I put.

Answer 16

I mean that swagmaster filled in the blanks well, but the exponent part is years, not days.
(Exponent is still the time, but not days. It's years)

Answer 17

The 15 I put in was years, who said it was days?

Answer 18

Me

Answer 19

Would it be 0.15 then...?

Answer 20

I don't seem to have a full ifno about what's going on overhere, but I think that's not a tragedy though.

Answer 21

full *info

Answer 22

Oh ok

Answer 23

So you don't know if I'm right or wrong?

Answer 24

So would the answer be 717445350 ?

Answer 25

3^15 = 14348907

14348907 x 50 = 717445350

Answer 26

@satellite73

Answer 27

so the population starts with 50 and triples every year

Answer 28

looks good to me!

Answer 29

So am I right?

Answer 30

@ganeshie8

Answer 31

if the calculation is correct, then yes

Answer 32

The answer would be f(x) = 50(3)^15 only?

Answer 33

thats an exponential function which models the snail population. you still need to explain what each number means and other details

Answer 34

50 is the amount of snails

3 is the average rate of change that is tripling.

15 is the amount of years.

Answer 35

we usually use "e" for continuous growth like poopulation but it should be okay i guess

Answer 36

f(t) = 50(3)^t

50 is the starting population of snails at t = 0

3 is the average rate of change that is tripling.

t is the number of years

Answer 37

that looks better^

Answer 38

Um, my function doesn't have t in it.

Answer 39

then replace t by x

Answer 40

f(x) = 50(3)^x

Answer 41

What about the 15? o.O

Answer 42

what about it ?

Answer 43

It's gone. :o

Answer 44

f(x) = 50(3)^15 <<

Answer 45

first of all, how did u get 15 ? i don't see it in the original question ?

Answer 46

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.

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 47

0-15 is the domain of your function

Answer 48

f(x) = 50(3)^x

is your exponential function and x can be any number between 0 and 15 (inclusive)

Answer 49

The question does not ask for domain ?

Answer 50

evaluating f(15) gives u the population of snails after 15 years

Answer 51

you can mention the domain is [0, 15] but don't let this technical detail confuse you

Answer 52

So the answer would still be.

f(t) = 50(3)^t

50 is the starting population of snails at t = 0

3 is the average rate of change that is tripling.

t is the number of years

Answer 53

that looks good but i thought you want to call the variable "x" ?

Answer 54

Oh, ok. xD

Answer 55

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 56

Is the answer to that one above g(x) = 200(1.0609) ?

Answer 57

I got that by doing '1.03^2'

Answer 58

do you mean g(x) = 200(1.03)^(2x) changes to g(x) = 200(1.0609)^x ?

Answer 59

Yes @ganeshie8

Answer 60

thats right ! interpret 200 and 1.03

Answer 61

Um, you mean interpret 200 and 1.0609?

Answer 62

yes they want you explain the key features of g(x)

` Then, explain to Iris how the key features of this local snail population compares to the key features of the invasive population.`

Answer 63

just compare the `starting population` and `growth rate` between the populations

Answer 64

I do not understand... ?

Answer 65

g(x) = 200(1.03)^2x

g(x) = 200(1.0609)

g(x) = 212.18

Is that correct? @ganeshie8

Answer 66

nope, g(x) is a function that models the local snail population

Answer 67

if you feed in x = 2, it gives you the predicted population after 2 years

Answer 68

g(x) = 200(1.0609)^x

lets round the number

g(x) = 200(1.06)^x

leave it like this

Answer 69

for the starting population, plugin x = 0, you get g(0) = 200(1.06)^0 = 200(1) = 200

Answer 70

1.06 tells you that the population is growing at a rate of 6% per year

Answer 71

which is very very slow compared to the invasive population growth rate which is 3 times (300% each year)

Answer 72

compare the starting populations similarly

Answer 73

invasive population is the function I created in the 1st question, correct?

Answer 74

yes

Answer 75

Their difference is 294 ?

Answer 76

what difference ?

Answer 77

yeah but thats not so much important i guess

Answer 78

stating 300% and 6% for the growth rates should be sufficient, explaining more would only impress your teacher :)

Answer 79

lol

Answer 80

yeah trust me highschool math teachers like it more when you explain using more sentences and use all your writing skills

Answer 81

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 82

Would the y-intercept be the average rate of change?

Answer 83

No wait, the y intercept would be the starting population.

Answer 84

`y intercept` is the value of y coordinate at which the curve cuts the y axis

Answer 85

it cuts the y axis when x = 0, so yes y intercept would be the starting population

Answer 86

graph both equations and see where they cut the y axis

Answer 87

https://www.desmos.com/calculator

Answer 88

who is 100(2)^x ?

Answer 89

your f(x) is 50(3)^x right ?

Answer 90

Is that correct? @ganeshie8

Answer 91

Oops my bad. xD

Answer 92

It would be (0, 50) ?

Answer 93

looks good !

https://www.desmos.com/calculator/xjqdco1cbe

Answer 94

Would the domain be all real numbers where 0 ≤ x ≤ ∞ is true ?

And the range is all real numbers where 0 ≤ y ≤ 50 is true ?

@ganeshie8

Answer 95

What's that link? @ganeshie8

Is (0, 50) wrong?

Answer 96

@ganeshie8 You there?