46 POINTS! BRAINLIEST! PLSSS HELP! ONLY ANSWER IF UR GUD AT MATH!


National Park Animal Populations

You are studying the populations of three animals in a national park. Below are the data sets for the animal populations. Circle the park that you chose:

Yellowstone

x Year

y1 Population 1, Grizzly Bears

(per square mile)

y2 Population 2, Pocket Gophers

(per square mile)

y3 Population 3, Osprey

(per square mile)

x y1 y2 y3

0 4.0 4.0 4.0

1 4.5 4.5 5.8

2 5.0 5.3 7.2

3 5.5 6.4 8.2

4 6.0 8.1 8.8

5 6.5 10.6 9.0

8 8.0 28.6 7.2

10 9.0 60.7 4.0


Everglades

x Year

y1 Population 1, American Alligator

(per square mile)

y2 Population 2, Marsh Rabbit

(per square mile)

y3 Population 3, Florida Panther

(per square mile)

x y1 y2 y3

0 6.0 6.0 6.0

1 6.5 6.5 7.8

2 7.0 7.3 9.0

3 7.5 8.4 9.8

4 8.0 10.1 10.0

5 8.5 12.6 9.8

8 10.0 30.6 6.0

10 11.0 62.7 1.0



Make Sense of the Problem

What do you want to find out?




Analyze the Data

Population 1 (y1): ______________________________ (Write the animal species' name.)

Answer the following questions about the growth function of population 1:

1. Is population 1 increasing or decreasing? (0.5 point)






2. What is the rate of change between year 0 and year 1 for population 1? What is it between year 5 and year 10? Include calculations in your answer. (2 points)







3. Predict the average rate of change from year 5 to year 6 for population 1. Use the average rate of change you found in question 2 in your prediction. (1 point)







4. What type of function best models the growth for population 1? Give a reason for your answer. (1 point)







Population 2 (y2): ______________________________ (Write the animal species' name.)

Answer the following questions about the growth function of population 2:

5. What is the maximum population per square mile during the first 10 years for population 2? (0.5 point)







6. What is the average rate of change for population 2 between years 5 and 10 (x = 5 to x = 10)? (1 point)







7. The average rate of change for population 2 changes by a common ratio (multiplication) of 1.5 each year. What type of function best models this growth? (1 point)







8. Estimate the average rate of change from year 5 to year 6 for population 2. Remember, the average rate of change for this population changes by a ratio of 1.5 each year. Show your work. HINT: First find the average rate of change from year 4 to year 5. (3 points)







Population 3 (y3): ______________________________ (Write the animal species' name.)

Answer the following questions about the growth function of population 3:

9. What is the maximum population per square mile during the first 10 years for population 3? In what year did this occur? (1 point)







10. What is the average rate of change for population 3 between years 5 and 10 (x = 5 to x = 10)? Show your work. Identify the change as an increase or a decrease. (2 points)







11. What type of function best models the growth for population 3? Give a reason for your answer. (1 point)







12. Use the graph provided. When do all three populations contain the same number of animals? (1 point)








13. Use the following graphs to verify your work on this question.


A. Estimate the average rate of change from year 5 to year 8 for population 3. Show your work. (2 points)







B. Estimate the average rate of change from year 8 to year 10 for population 3. Show your work. (2 points)







C. Based on the answers to Parts A and B, estimate the number of animals in population 3 in year 15, and give a reason for your estimate. (1 point)

Yellowstone

What do you want to find out?

-What type of function best models the population growth for each species

Population 1 (y1):

Grizzly Bears

1. Increasing

2. (4.5-4.0)/(1-0) =0.5

3. 0.5. The rate of change between year 5 to year 6 is the same as that between year 0 to year 1.

4. Linear

Population 2 (y2):

Pocket Gophers

5. 60.7 population per square mile

6. (60.7-10.6)/(10-5) =50.1/5 =10.02

7. Exponential

8. From year 4 to year 5, (10.6-8.1)/(5-4) =2.5

The estimated rate of change from year 5 to year 6:

2.5 x 1.5 =3.75

Population 3 (y3):

Osprey

9. 9 population per square mile. This occurred in year 5.

10. (4-9)/(10-5) =-5/5 =-1

This is a decrease

11. Quadratic, the numbers increase as well as decrease.

12. Circle the point where x=0 (the point where the three lines intercept)

The initial point, where x=0, y1,y2,y3 =4

13. A. (7.2-9)/(8-5) =-1.8/3 =-0.6

B. (4-7.2)/(10-8) =-3.2/2 =-1.6

C. (-1.6)-(-0.6)/(10-5) =-0.2

the formula is

-0.2*(x^2)+2x+4

Substituting x with 15,

-0.2*(15^2)+2(15)+4

=-45+30+4

=-11 population per square mile

Answer:

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