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43 votes
8.

The table shows the estimated number of deer living in a forest over a five-year period. Are the data best represented by a linear, exponential, or quadratic model? Write an equation to model the data.


A. quadratic; y = 0.79x2 + 98

B. linear; y = 0.79x + 98

C. quadratic; y = 98x2 + 0.79

D. exponential; y = 98 • 0.79x

8. The table shows the estimated number of deer living in a forest over a five-year-example-1
User Arseny
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1 Answer

9 votes
9 votes

Answer:

D. exponential; y = 98 • 0.79x

Explanation:

Answer:

Option D is correct.

Exponential model are the data best represented.

Equation:

Step-by-step explanation:

An exponential function is in the form of .....[1] where a is the initial value and b≠0 , b > 1.

Consider any two points from the table;

(0, 98) and ( 1, 77)

Then substitute these in [1];

For (0, 98)

x = 0 and y = 98 substitute in [1] we get;

98 = a

Similarly, For (1, 77)

we have;

77 = ab

Substitute the value of a =98 we get;

Divide both sides by 98 we get;

⇒ b = 0.79

We get an equation;

Therefore, the data represent here is, Exponential function.

also, an equation to model the data is;

...............................................................................................................................................

All the functions grow with x except B that decreases when x grows. That i your function. Also check that when you divide the population of two consecutive years, the ratio remains 0.79 approx

The solution is D

...............................................................................................................................................

Exponential would be the correct answer I believe...

...............................................................................................................................................

For a better understanding of the explanation provided here please find the attachment.

The solution will employ the use of the trial and error method and basic math.

As can be see from the given data, the deer population keeps on falling from the year zero. Thus, we can safely conclude that the quadratic and the linear models will not represent the situation at all.

We are left with the exponential model and since we have in it we can see that the deer population will fall as the years pass.

We have checked it in the table that has been provided and we have concluded that the data is best represented by the exponential model because when the exponential formula is applied it is almost equal to the actual number of deers.

Please check the attached table for a better understanding.

8. The table shows the estimated number of deer living in a forest over a five-year-example-1
User Jim Dennis
by
3.1k points