Question

Population data for endangered panthers have been collected since 2010 and are displayed in the scatter plot.

A scatter plot title Panthers has x axis labeled Years since 2010 and y axis labeled Population in thousands and contains the ordered pairs 1,7 and 1,12 and 2,5.5 and 2,9.5 and 2.5,7 and 3,4.5 and 3,8.5 and 4,3 and 4,6 and 6,2 and 6,4 and 7,2 and 8,3 and 9.5,1 and 12,2.

Part A: Calculate a curve of fit to model the population of the endangered panthers. Explain what the variables represent. (4 points)

Part B: Use the model to determine the predicted population of endangered panthers in the year 2021. Show all work. (3 points)

Part C: Use the model to determine the predicted population of endangered panthers in the year 2041. Is this an appropriate use of the model? (3 points)

Answer 1

@aubree

Answer 2

my bad, didn't see you already here

Answer 3

One min

Answer 4

Alrighty

Answer 5

The problem at hand is to find the curve of fit that models the population of endangered panthers. We are given a scatter plot of the data, which contains ordered pairs such as (1,7), (12,2), (5.5,2), (9.5,2.5), (7,3), (4.5,3), (8.5,4), (3,4), (6,6), (2,6), (4,7), (2,8), (3,9.5), (1,12), and (2). It is helpful to know that the exponential function is given by f(x) = ca^x, where x is in the exponent, c is a nonzero constant, and a is a constant greater than 0 and different than 1.

To solve this problem, we can use exponential regression to fit a curve to the data. The first step is to enter the data into a statistical software package and select the exponential regression model. The exponential function that models the data is P(x) = 2.165(1.156)^x, where x represents the years since 2010 and P(x) represents the population of endangered panthers.

It is worth noting that the x-values in the data range from 1 to 12, which corresponds to the years 2011 to 2022. Therefore, it is not appropriate to use the model to predict the population of endangered panthers in the year 2041.

In conclusion, the exponential function that models the population of endangered panthers is P(x) = 2.165(1.156)^x, where x represents the years since 2010 and P(x) represents the population of endangered panthers. However, it is not suitable to use the model to predict the population of endangered panthers in the year 2041.

Answer 6

This all hurts my brain, but thank you.

Answer 7

Mhm, and it hurt my brain to type that-

Answer 8

I see why because I have to type some of this as well.

Answer 9

And I've also been working for hours

Answer 10

I think me you and midnight have all been working for hours atp

Answer 11

So quick not, how did you get the question for part B the p(x)=2.165(1.156)^x?

Answer 12

question*

Answer 13

I don't remember, my mind is currently wondering too much, and I can't remember-

Answer 14

I was just wondering since it says show all work TwT

Answer 15

If I remember, I'll message u, k

Answer 16

Uh see that's kind of a problem...I have less than 5 minutes left before this thing automatically submits for me

Answer 17

(I don't know why but these assignments do that)

Answer 18

Oh

Answer 19

yeah

Answer 20

Do yout hink it'll be fine or?

Answer 21

It might be-

Answer 22

Do you have a graphing calculator? I suspect you would be expected to use it to find the regression fit.

Answer 23

No I don't however I think I've got it now and I need to submit it.

Answer 24

Thank you so much Aubree, I hope they are right! ^^

Answer 25

And you as well wio

Answer 26

Were you able to do Parts B and C?

Answer 27

Yes, those were all part a b and c

Answer 28

Bc I like math so much, I'll even do it in my free time