Respuesta :

Answer:

Option B

Step-by-step explanation:

Given is a table of t no of years and N(t), number of coyotes reported.

The table follows a functional pattern and we have to find the correct one out of given three.

For that we can find N(t) using the function and compare with the given table. Which shows less variation would be the answer.

         

No of coyotes reported        

        Total

t 0 1 2 3 4 5 6  

N(t) 1 2 4 7 14 28 55  

Function I 0.5t^2+1 1 1.5 3 5.5 9 13.5 19  

Differenc  0 -0.5 -1 -1.5 -5 -14.5 -36 -58.5

2 1.95^t 1 1.95 3.8025 7.414875 14.45900625 28.19506219 54.98037127  

Difference  0 0.05 0.1975 -0.414875 -0.45900625 -0.195062187 0.019628734 -0.801814703

3 0.5t^3-t^2 +5t+1 1 5.5 11 20.5 37 63.5 103  

Difference  0 -3.5 -7 -13.5 -23 -35.5 -48 -130.5

We find that the difference is the least for   option B.

Option B is the right answer.

The function that correctly models the data is [tex]N(t) = 1.95^{t}[/tex]

In order to determine which function best fits the data, we would solve for time 1 and 6.

[tex]N(t) = 0.5t^{2} + 1[/tex]

Year 1 = 0.5(1)² + 1  

Year 1 = 0.5 + 1

Year = 0.6

Time 6 =  0.5(6)² + 1  

= 18 + 1

= 19

This function doesn't model the situation.

[tex]N(t) = 1.95^{t}[/tex]

[tex]N(1) = 1.95^{1}[/tex]

= 1.95

[tex]N(6) = 1.95^{6}[/tex]

= 54.98

This function closely models the situation.

[tex]N(t) = 0.5t^{3} - t^{2} + 0.5t + 1[/tex]

[tex]N(1) = 0.5(1)^{3} - (1)^{2} + 0.5(1) + 1[/tex]

= 1

[tex]N(6) = 0.5(6)^{3} - 6^{2} + 0.5(6) + 1[/tex]

= 76

This function does not model the situation.

[tex]N(t) = 2t + 1[/tex]

[tex]N(1) = 2(1) + 1[/tex]

= 3

[tex]N(6) = 2(6) + 1[/tex]

= 13

This function does not model the situation.

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