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

Answer:

 

exponential; y = 89 • 0.62^x

Step-by-step explanation:

Answer 2

Answer:

Option B exponential y = 89 · 0.62x

Step-by-step 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 = $\frac{55}{89}$ = 0.618

r = $\frac{34}{55}$ = 0.618

so it can be represented by an exponential model.

$y=a (r) ^{x}$

$y=89(62) ^{x}$

Option B is the answer.