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Answer:
Therefore the width is 25 feet for getting maximum area.
The maximum area of the rectangle is 625 square feet.
Therefore the range is 0≤A≤625.
Step-by-step explanation:
Given function is
A = - x²+50x
We know that ,
If y = ax²+bx+c
For the maximum
Here a = -1 , b= 50 and c=0
Therefore the width
Therefore the width is 25 feet for getting maximum area.
The maximum area =[ -(25)²+50.25] square feet
= 625 square feet
The area can not be negative and maximum area is 625 square feet.
Therefore the range is 0≤A≤625.
The population function of the Western Lowland Gorillas can either represent population growth or population decay
<h3>How to model the population</h3>The question is incomplete, as the resources to model the population of the Western Lowland Gorillas are not given.
So, I will give a general explanation to solve the question
A population function can be represented as:
Where:
- The initial population of the Western Lowland Gorillas is represented by (a)
- The rate at which the population changes is represented by (r)
- The number of years since 2022 is represented by (x)
- The population in x years is represented by (y)
From the question, we understand that the population of the Western Lowland Gorillas decreases.
This means that the rate of the function would be an exponential decay i.e. 1 -r
Take for instance:
By comparison.
a = 2000 and 1 - r = 0.98
The above function can be used to model the population of the Western Lowland Gorillas
Read more about exponential functions at: