Question

someone please help with algebra 1!!!!

Answer 1

Okay?

Answer 2

wats your question

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.

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.


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.


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.


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 4

?? please help

Answer 5

somebody? for a medal??

Answer 6

idk sorry

Answer 7

could you tag someon who can?

Answer 8

idk who

Answer 9

could someone please help?

Answer 10

@ranga is the man for you.

Answer 11

@ranga please help?

Answer 12

??? @ranga

Answer 13

Exponential growth function looks like: y = A * (1+r)^x
Here, A would be the initial population and r would the rate of growth.
You can pick some numbers. Let there be 100 snails to start with and let the rate of growth be 5%. Then A = 100 and r = 0.05. Plug it into the equation:
y = 100 * (1+0.05)^x
y = 100(1.05)^x where x is the time in years and y is the snail population.

Answer 14

thats for the first problem?

Answer 15

how would i do the next one?

Answer 16

For the first problem also include that domain of the function is [0,15] because they say it is an exponential growth for 15 years and so the formula is good only for the first 15 years.

Answer 17

okay i will.

Answer 18

\[\Large g(x) = 200(1.03)^{2x} = 200((1.03)^2)^x = 200(1.0609)^x\]

Answer 19

We have converted the function with exponent 2x to just x above.
g(x) = 200(1 + 0.0609)^x
Compare this to the general function stated in the first part: y = A(1+r)^x
We find A = 200 and r = 0.0609.
Therefore the initial snail population here is 200 and the rate of growth is 0.0609 or 6.09%

Answer 20

okay so the third one?

Answer 21

From part 1) we have f(x) = 100(1.05)^x
when x = 0, f(x) = 100(1.05)^0 = 100. This is the y-intercept which represents the starting population. Every year the population increases by 5% and therefore this function will always be increasing. The domain is x = 0 to x = 15 because it is given in the problem:
"She has observed that the population follows an exponential rate of growth for fifteen years."

Domain is [0, 15]
To get the range put x = 0 and x = 15 and calculate f(x).
f(0) = 100(1.05)^0 = 100
f(15) = 100(1.05)^15 = 207.89 rounded down to 207 because number of snails has to be a whole number.
So range is [100, 207]

Answer 22

For the last part, the average rate of change between years x = 2 and x = 5 is:
{ f(5) - f(2) } / { 5 - 2 } = ?
I will let you calculate the average rate using the above formula.
What the average rate here represents would be the average number of increase in snail population each year between the years 2 and 5.

Answer 23

so thats all the problems then? thats all i have to do? seems simple enough! thank you so much!

Answer 24

You are welcome.

Answer 25

for the last one would the vaerage rate of change be 3/3

Answer 26

??

Answer 27

Not 3/3.
f(x) = 100(1.05)^x
f(5) = 100(1.05)^5 = ?
f(2) = 100(1.05)^2 = ?
Plug the numbers into the formula:
Average rate of change between years x = 2 and x = 5 is: { f(5) - f(2) } / { 5 - 2 }

Answer 28

127.628-110.25/3?

Answer 29

Yes. But simplify the number and round it.