Question

Halp!

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

@jim_thompson5910 @undeadknight26 @agent0smith

Answer 3

Hello Im emily im here to help :)

Answer 4

just give me a sec to wright it down for ya okay?

Answer 5

Hi!

Answer 6

thank you :)

Answer 7

Seariously this is the only way I know to explain the snail one its easier than it looks
Here is some ideas to think about for this problem.
First consider that the formula f(x) = P (1 + r) ^x.
is the formula used for compound interest.
in a bank if you invest $1 and the APR (annual percent rate) is 5% will you will end up with
$1,05 at the end of the year ? ... YES, NO, MAYBE ???
The first consideration in this case is that you have to get at least your dollar back ...
That is where the "1 +" comes in to play... now for you extra money (the interest) that is the "r"
In my stort it would be 5% (.05)... so if you keep th emoney in there for one yeat you get 1(1+.05)^1
or 1.05 ... now the compounding ... if you keep it there for a second yeat then the total is
1(1.05)(1.05) OR .... 1(1.05)^2

Now if the compounding is more than once a year (lets say quarterly) then the compounding periods has to be multiplied by 4 and the rate has to be divided by 4

1(1 + .05/4)^ 2*4 for two years...

the number of compoundings can be any number...
Now ther is a SPECIAL situation where there is a infinite compoundings per year (and NO you do not end up with an infinite amount of money)
when done the equation produces a special number "e" (2.71...)
this is called continuoue compounding... this actually will model things like radioactive decay
f(x)= P e^r

bottom line here is if the snals reproduce continuously you would use the "e" formula...
f(x) = P (1 + r) ^x.
where r is the percent increase in population each cycle and x is the time interval of each cycle
if the reproduction is at a steady interval then you can use the

Answer 8

#2 ok..do like this g(x)=(200)x(1.03)x(2)x=(200)x(2.06)x=412x so..this is an equation of the form g(x)=cx..yu can plot this on graph as mentioned earlier by subsituting different values of x

Answer 9

#3 after plotting the graph ,yu will get to know everything...i mean every answer...just plot the graph yurself and then show me ...i will help you with the rest of questions
if yu will take integer values of x like 1 ,2 ,3 ... ,then the graph will be too big to plot on paper...yu should subsitute values like x=0.1 ,0.2 ... and the respective y values will be 41.2 ,82.4 ....this way plot the graph
just check the minimum value of g(x) from the graph and maximum value too...the will be the range

Answer 10

#4 first calculate value of g(x) for 2 yrs and then for 5 yrs and then the change will be the ratio of change in g(x)/change in x i:e 3

Answer 11

and my hands hurt...

Answer 12

did that help?

Answer 13

How do you write so fast lol

Answer 14

typing classes since 6th grade :)

Answer 15

yea it helped like so much thank you

Answer 16

Yeah np and if ya need hale tag me kay?

Answer 17

*help

Answer 18

and lol I was never a fan of typing

Answer 19

ok thank you so much!

Answer 20

same lol till my mom put me at the computers and well i went from there lol

Answer 21

No problem :)

Answer 22

*hand cramp*

Answer 23

Can you make #1 a wee bit shorter please? @Emllyk