Question

These lessons are a total blur will some one help

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.
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.
____________________________________________________________________________
Gordon is evaluating some stocks he wants to purchase. You can see the function of the stock price below. The variable x represents days.
Stock
A
B
C
Price
f(x) = 25(1.08)x

x
f(x)
0
22.00
1
21.56
2
21.13


The initial price of this stock is $30, but it has been increasing 4% each day.
Create the price function for Stock D. It should have the second lowest starting price and the second highest rate of growth. Using complete sentences, justify that your function meets these requirements.
Graph the price function for Stock D. Explain the key features of the graph with complete sentences.
A recent drop in sales has affected Stock D with the function g(x) = –6. Explain to Gordon how Stock D’s new price function, f(x) + g(x), will be created. Graph f(x) + g(x).
Gordon wants to fully understand what kind of changes could affect the money he is investing. Using complete sentences, explain the effect of the following transformations. Graph them and f(x) on the same coordinate plane.
f(x + 2)
f(–x)
f(x) + 3

Answer 2

@danish071996

Answer 3

@Michele_Laino

Answer 4

question #1
a possible exponential function, can be this:

\[\Large f\left( x \right) = k \times {B^x}\]
where k and B are two constants

Answer 5

and x can be the number of years

Answer 6

question #2
we have the subsequent steps:
\[\Large {1.3^{2x}} = {\left( {{{1.3}^2}} \right)^x} = {1.69^x}\]
so we can write:
\[\Large g\left( x \right) = 200 \times {1.69^x}\]

Answer 7

question #3
referring to f(x), we have:
x is the number of years, so if we set x=0, we get:
f(x)=k, and k is the number of snails at the starting year of observation

Answer 8

@Jasmiinnee_m what do you think?

Answer 9

So far so good.

Answer 10

@Michele_Laino

Answer 11

but most of these questions want more then just an expresion

Answer 12

question #4
here we have to use the function g(x), so the requested average rate r of change, is given by the subsequent formula:
\[\Large r = \frac{{g\left( 5 \right) - g\left( 2 \right)}}{{5 - 2}} = ...\]
please substitute the formula for g(x), namely:
\[\Large g\left( x \right) = 200 \times {1.69^x}\]
and simplify that average rate r

Answer 13

what do you get? @Jasmiinnee_m

Answer 14

Honestly I have no Idea how to solve that....

Answer 15

hint:
\[\Large \begin{gathered}
r = \frac{{g\left( 5 \right) - g\left( 2 \right)}}{{5 - 2}} = \frac{{200 \times {{1.69}^5} - 200 \times {{1.69}^3}}}{3} = \hfill \\
\hfill \\
= \frac{{200 \times {{1.69}^3}\left( {{{1.69}^2} - 1} \right)}}{3} = ... \hfill \\
\end{gathered} \]

Answer 16

\[\large \begin{gathered}
r = \frac{{g\left( 5 \right) - g\left( 2 \right)}}{{5 - 2}} = \frac{{200 \times {{1.69}^5} - 200 \times {{1.69}^3}}}{3} = \hfill \\
\hfill \\
= \frac{{200 \times {{1.69}^3}\left( {{{1.69}^2} - 1} \right)}}{3} = ... \hfill \\
\end{gathered} \]
please continue

Answer 17

666?

Answer 18

I got:
r=597.3

Answer 19

oh

Answer 20

Thank you but what about the other ones

Answer 21

hint:
the price at day x=0, is $30
at day x=1, price is 30(1+0.04)
at day x=2 the price is 30(1+0.04)^2
so what can you conclude?

Answer 22

@Jasmiinnee_m

Answer 23

which question is this for?

Answer 24

@Michele_Laino

Answer 25

it is the question bout the stock price functions

Answer 26

oh um

Answer 27

I mostly dont understand how to write it all now

Answer 28

@Michele_Laino