Question

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.

0/89 1/55 2/34 3/21 4/13


a. quadratic; y = 0.62x2 + 89

b. exponential; y = 89 • 0.62x

c. linear; y = 0.62x + 89

d. quadratic; y = 89x2 + 0.62

Answer 1

exponential; y = 89 • 0.62^x

Explanation:

Answer 2

Option B exponential y = 89 · 0.62x

Explanation:

The table shows the estimated number of deer living in a forest over a five year period.

Year Number of deers

0 89

1 55

2 34

3 21

4 13

Now we have to find the model representing this situation. Difference in number of deer, in the forest.

We can see there is a common ratio between each successive term r =
`(55)/(89)` = 0.618

r =
`(34)/(55)` = 0.618

so it can be represented by an exponential model.

`y=a (r) ^(x)`

`y=89(62) ^(x)`

Option B is the answer.