Question

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

Answer 1

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

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 =
`(f(18) - f(0))/(x_(2) - x_(1) )`

Average =
`(9.1 - 8.3)/(18 - 0)`

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 =
`(f(18) - f(0))/(x_(2) - x_(1) )`

Average =
`(68.7 - 0)/(18 - 0)`

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.