Step-by-step explanation:
Suppose that the carrying capacity is 900 fish, the intrinsic growth rate is equal to 2, and the harvest rate is 20%.
a. Use the graphical or eigenvalue approach
Answer:
24000
Step-by-step explanation:
Answer:
The length of the longer base he 35 units
Step-by-step explanation:
Here, we want to find the length of the longer base of the trapezoid
Mathematically, we can find the area using the formula;
1/2( a + b) h
where a is the shorter base
b is the longer base
h is the height
Let the shorter base be x
The other base is 5 times this length and that makes 5 * x = 5x
Height is the average of both bases;
(x + 5x)/2 = 6x/2 = 3x
Substituting these in the formula, we have ;
1/2(x + 5x)3x = 441
3x(6x) = 882
18x^2 = 882
x^2 = 882/18
x^2 = 49
x^2 = 7^2
x = 7
But the longer base is 5x and that will be 5 * 7 = 35 units
First, note that

is always positive (except for x=0), so

must be always negative.
Thus, the only plausible graphs are 1 and 3 since they are below the x-axis.
Now,

and

are only defined for x≥0, because only for these x'es we can take the square root.
Note that the third graph has domain (-infinity, 0], so it is not the right one, while 1 is ok.
Answer: first graph