25. Michael is studying population changes in two

types of birds living on an island. Compare the

populations by finding and interpreting the

average rates of change over the interval [0, 18]

Bird A

Time(months):

6

12

18

Population:

(thousands)

8.3

8.6

8.8

9.1

Bird B

y= 3.6(1.06)x

Average rates of change for Bird A is 0.045 and for Bird B is 3.816.

Step-by-step explanation: Through its graph, a function can be analyzed and be identified its attributes. Average Rate of Change is the ratio of change in the function values to the change of x-value, i.e., it is the slope of the function in a specific interval of x. With the Average it is possible to compare two function.

Average Rate of Change

Bird A:

For the interval [0,18]:

x₁ = 0 f(0) = 8.3

x₂ = 18 f(18) = 9.1

Average =

Average =

Average = 0.045

Bird B: y = 3.6(1.06)x

For the interval [0,18]:

x₁ = 0 y = 3.6(1.06)0 = 0

x₂ = 18 y = 3.6(1.06)18 = 68.7

Average =

Average =

Average = 3.816

The Average Rate for Change for Bird A is 0.045 and for Bird B is 3.816. This means that the population of Bird B increase in rate faster than the population of Bird A.

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x