Question

What kind of growth model (pattern) is shown in the table?

x y
1 5
2 25
3 125
4 625
5 3,125

a. square root
b. linear
c. exponential
d. quadratic

Answer 1

it is showing exponential growth in the graph

Answer 2

Option C is correct.

The kind of growth model is shown in the table is exponential

Explanation:

Exponential growth function is in the form of :
`y = ab^x` ......[1]; where a is the initial value and b> 0.

Consider any two point from the table:

(1 , 5) and ( 2 , 25)

Substitute these in the equation [1] we get;

`5 = ab^1` ......[2]

`25 = ab^2` ......[3]

Divide equation [3] by [2] we have;

`(25)/(5) = (ab^2)/(ab)`

Simplify:

`5 = b`

Now substitute this value in equation [2] we get;

`5 = a * 5`

Divide both sides by 5 we get;

`(5)/(5) = (5a)/(5)`

Simplify:

1=a or a = 1

Therefore, the table shown the exponential growth function is,
`y = 5^x`