Question

@SolomonZelman I need to check my answer and I have two other parts that I need help with.

Answer 1

Yes, how may I help you ?

Answer 2

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.

15 years when x is equal to the time unit. So 15 is equal to x.
We don’t have P so let’s have 200 as P and let’s say that the rate doubles each year so we will have .5.

P = amount you start with
R = rate
X = time

f(x) = p(1 + r)^x
f(15) = 200(1 + 0.5)^15
f(15) = 200(1.5)^15
f(15) = 200(437.893890380859)
f(15) = 87578.7780761718 This will be the snail population in 15 years. The solution is irrational.


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(1.03^2)^x
g(x) = 200(1.0609)^x
g(x) = 212.18 This solution is irrational.

Both solutions for the local and invasive are irrational.

Answer 3

Are these correct?

Answer 4

Lets start from here,

P is the y-intercept
R is the slope
X (not the lower case x, but the one you wrote next to `P` and `R`) is the `f(x)` itself

Answer 5

No

Answer 6

X is the x.

Answer 7

And r is the rate of an EXPONENTIAL FUNCTION.

Answer 8

I know what you did incorrectly, I'll post the convertion

Answer 9

Well it didnt give me P or R so I pluged in 200 for P and 0.5 for R and my tutor said that it was correct, I just wanted to check the second one.

Answer 10

\(\large\color{midnightblue}{ \rm g(x) = 200(1.03)^{2x} }\)

\(\large\color{midnightblue}{ \rm g(x) = 200(1.03^2)^{x} }\)

\(\large\color{midnightblue}{ \rm g(x) = 200(1.0609)^{x} }\)

and where is 212.18 from ?

Answer 11

200(1.0609) = 212.18 right?

Answer 12

This is only when x=1

Answer 13

so what is x?

Answer 14

Assuming that each x unit is a year, this would be CORRECT, for ONE YEAR.

Answer 15

Oh wait, it is 15 years for the first one so it has to be 15 years for this one as well

Answer 16

It depends, on the question,

\(\large\color{midnightblue}{ \rm g(x) = 200(1.0609)^{x} }\)

(which is same as \(\large\color{midnightblue}{ \rm g(x) = 200(1.03)^{2x} }\) )

IS for how many years ?

Answer 17

I would think that it is asking you for a 15-tear period.

Answer 18

\(\large\color{midnightblue}{ \rm g(x) = 200(1.0609)^{x} ~~⇒~~ g(x) = 200(1.0609)^{15}~~⇒~~? }\)

Answer 19

you can find 15 by graphing x=15 and seeing where the curve and x=15 intersect.

Answer 20

or just calculate it as I showed ... tell me if you need more help

Answer 21

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 22

heres the graph that I have @SolomonZelman

Answer 23

how in the world do you get a line ?

Answer 24

sorry about the world ;)

Answer 25

i graphed the function and that is how it came up..

Answer 26

Y = 200(1 + 0.5)^15

Answer 27

It has a y-intercept of 87578.78 and a zero slope. The function is increasing because the snail population grows.

Answer 28

@SolomonZelman

Answer 29

I graphed the function in red

x=15 in blue

and the intersection point is labeled in black

https://www.desmos.com/calculator/kztgaj4doi

Answer 30

Thanks! :)

Answer 31

Anytime !