Question

16

fy
What is the rate of change of the function shown on the
graph? Round to the nearest tenth.
14
(2. 12.5)
12
10
O 2.00
O 2.50
O 5.25
O 10.50
8
6
(1,5)
4
(-1,0.8) 3 (0,2)
-4 -3 -2 -1
-2
4 x
-4
-6

Answer 1

`2.50`

Explanation:

Given

`(x_1,y_1) = (-1,0.8)`

`(x_2,y_2) = (0,2)`

`(x_3,y_3) = (1,5)`

`(x_4,y_4) = (2,12.5)`

Required

The rate of change (b)

The above graph is represented as:

`y = ab^x`

For:
`(x_2,y_2) = (0,2)`;

We have:

`y = ab^x`

`2 = a * b^0`

`2 = a *1`

`2 = a`

`a = 2`

For
`(x_3,y_3) = (1,5)`,

We have:

`y = ab^x`

`5 = a * b^1`

`5 = a * b`

Substitute
`a = 2`

`5 = 2 * b`

Divide by 2

`2.5 = b`

`b = 2.5`

Hence, the rate of change is 2.50