Question

Help Please.. Will Give Medal !! Project thing

Answer 1

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.
 
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.
 
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.
 
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.

Answer 2

@zepdrix Hi, Can you help me with this please ?

Answer 3

@jim_thompson5910 Can you help me out please ?

Answer 4

it seems like #1 can't be done without data to back it up, so I'll skip that

Answer 5

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 6

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

g(x) = 200( 1.03^2 )^x ... using the rule: a^(b*c) = (a^b)^c

g(x) = 200( 1.0609 )^x

Answer 7

As for the comparison, that relies on #1, but I skipped that part because I don't have the data.

Answer 8

Okay Thanks

Answer 9

Is that enough to finish up the project?

Answer 10

Well how would you do 3 and 4... You can just explain how to do it

Answer 11

for #3, you would use a graphing calculator or some other graphing tool (like geogebra) to graph the function you find in part #1

Answer 12

On #1 you can use any data for 15 years

Answer 13

the proper domain and range is the set of positive real numbers because you can't have negative time or growth

Answer 14

so you make it up completely?

Answer 15

Yes

Answer 16

ok, well if that's the case, then we could make up points that lie on say the function

f(x) = 50(1.27)^x

Answer 17

so when x = 0, f(x) = 50

when x = 1, f(x) = 63.5

etc etc

Answer 18

you could graph these points by hand and then draw a curve through them

but it's better to use graphing tools (like geogebra)

Answer 19

Okay... so then to add the time (15 years) you would just substitute x with 15, right ?

Answer 20

correct

Answer 21

Okay thank you very much.. You helped me understand this

Answer 22

you're welcome, I'm glad it's making more sense now

Answer 23

I can help more :)
Here you go for those who are looking for the right answers. (If you can't view the document then the Q&A's are below. Although it is recommended you view the document for better understanding. I will also attach it as a pdf file.)

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.

This is the formula that is used to show exponential growth over time: f(x) = P(1 + r)x.
Now I need to create an equation based off of the information given, and in the form of the equation above.
Because I wasn't told what the initial population of the snails was I need to make a value for the initial population of the snails; an appropriate value. So let’s say that the initial population of snails was 150. Let’s also say that the rate of growth is 50%; because we weren't given this information to begin with. Now that we have a value for P and r we can plug in the values.
F(x) = 150(1 + 0.5)x
P represents the initial population.
R represents the rate of growth.
X represents the number of years.

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.

G(x) = 200(1.03)2x
G(x) = 200(1.032)x
G(x) = 200(1.0609)x

First let’s start off by mentioning the key features. As you can see the local snails initial population is 200, whereas the initial population for the invasive snails is 150. Also, if you take a look at the exponential function above you may notice that g(x) = 200(1.0609)x can also mean g(x) = 200(1 + 0.0609)x. This means that the rate of growth for the local snails is 6.9%, whereas the growth rate for the invasive snails is 50%. So the local snails began with a larger population than the invasive snails, but the invasive snail’s growth rate is much larger than the local snail’s growth rate.





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.

F(x) = 150(1 + .5)x
Let’s plug in some values for x! Earlier Iris mentioned that she observed the snail’s growth for 15 years. So we can graph the population of the snails for all 15 of those years using the exponential function we made earlier. Starting at year 0, and ending at year 15.
F(0) = 150(1 + .5)0
F(0) = 150(1.5)0
F(0) = 150(1)
F(0) = 150
This means that at year 0, or the beginning, the snail population was 150. Now all we have to do is the same thing for year 1 to year 15. These should be our results:
F(0) = 150
F(1) = 225
F(2) = 337
F(3) = 506
F(4) = 759
F(5) = 1139
F(6) = 1708
F(7) = 2562
F(8) = 3844
F(9) = 5766
F(10) = 8649
F(11) = 12974
F(12) = 19461
F(13) = 29192
F(14) = 43789
F(15) = 65684
What those mean is after 15 years [f(15)], the population of invasive snails is 65, 684. Now that we know what these represent and their values we can start to set their ordered pairs and plot them on a coordinate plane. These are the ordered pairs:
(0, 150) (1, 225) (2, 337) (3, 506) (4, 759) (5, 1139) (6, 1708) (7, 2562) (8, 3844) (9, 5766)
(10, 8649) (11, 12974) (12, 19461) (13, 29192) (14, 43789) (15, 65684)
The domain for this function would be 0≤x≤15 and the range for this function is 150≤y≤65684. The y-intercept of this function is 150. This function is increasing.


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.

So, to find the average rate of change for a function you use this formula.
(F(b)-F(a))/(b-a)
When f(b) and f(a) represent the output values, and b and a represent the input values. So this is how it would look for this scenario.

(F(5)-F(2))/(5-2)
(1139 -337)/3
802/3
267/1
This means that the average rate of change in this function from year 2 to year 5 is about 267. What the means is the population of invasive snails, on average, increased by 267 each year from year 2 to year 5.