Answer:
(a) 20 represents the initial population and
1.014 represents 1 + % growth of rabbits each day
(b) Average Rate of change = 0.8
Step-by-step explanation:
P.S - The exact question is -
Given - A population of rabbits in a lab, p(x), can be modeled by
the function p(x)=20(1.014)^x, where x represents the number
of days since the population was first counted.
To find - (a) Explain what 20 and 1.014 represent in the context of
the problem.
(b) Determine, to the nearest tenth, the average rate of
change from day 50 to day 100.
Proof -
(a)
Given that the function p(x) is represented as
[tex]p(x) = 20(1.014)^{x}[/tex]
Here,
20 represents the initial population and
1.014 represents 1 + % growth of rabbits each day
(b)
Given,
[tex]p(x) = 20(1.014)^{x}[/tex]
When x = 50
[tex]p(50) = 20(1.014)^{50}[/tex] = 40.08000 ≈ 40.1
When x = 100
[tex]p(100) = 20(1.014)^{100}[/tex] = 80.32033 ≈ 80.3
Now,
Average Rate of change = [tex]\frac{p(100) - p(50)}{100 - 50}[/tex]
= [tex]\frac{80.3 - 40.1}{50}[/tex]
= [tex]\frac{40.2}{50}[/tex]
= 0.804 ≈ 0.8
⇒Average Rate of change = 0.8
