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Answer:
The y-intercept of the function is: b=10
Step-by-step explanation:
Given the table
x y
1 8
2 6
3 4
4 2
Taking any two points to find the slope
- (1, 8)
- (2, 6)
The slope between (1, 8) and (2, 6) is:
We know that the slope-intercept form of the line equation is
where m is the slope and b is the y-intercept.
Substituting m=-2 and any point i.e. (1, 8) in the slope-intercept form of the line equation to find the y-intercept (b).
8 = -2(1) + b
8 = -2 + b
b = 8+2
b = 10
Thus, the y-intercept of the function is: b=10
Answer:
The water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.
Step-by-step explanation:
Let , for
.
represents the temperature of the water, measured in degrees Celsius, and
is the number of salmon swimming upstream to spawn, dimensionless.
We compute the first and second derivatives of the function:
(Eq. 1)
(Eq. 2)
Then we equalize (Eq. 1) to zero and solve for :
And all roots are found by Quadratic Formula:
,
Only the first root is inside the given interval of the function. Hence, the correct answer is:
Now we evaluate the second derivative at given result. That is:
According to the Second Derivative Test, a negative value means that critical value leads to a maximum. In consequence, the water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.