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.

This is the table :
Year Estimated Population
0 98
1 77
2 61
3 48
4 38


A. Quadratic; y=0.79x^2 + 98

B. Exponential; y=98 * 0.79^x

C. Quadratic; y=98x^2 +0.79

D. Linear; y=0.79x+98

Answer 1

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 B

Answer 2

Option B is correct.

Exponential model are the data best represented.

Equation:
`y = 98 \cdot (0.79)^x`

Explanation:

An exponential function is in the form of
`y= ab^x` .....[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 =ab^0`

98 = a

Similarly, For (1, 77)

we have;

`77 =ab^1`

77 = ab

Substitute the value of a =98 we get;

`77 = 98b`

Divide both sides by 98 we get;

`(77)/(98) = (98b)/(98)`

⇒ b = 0.79

We get an equation;
`y = 98 \cdot (0.79)^x`

Therefore, the data represent here is, Exponential function.

also, an equation to model the data is;
`y = 98 \cdot (0.79)^x`