Let x be the number of times they raise the price on the newspaper. Then the new cost of the newspaper is

Let y be the newspaper they sell, then the income will be

Now, we know that the circulation is of 500, assuming that they sold every newspaper at the original price now the number the will sell will be

Plugging the value of y in the first expression we have that the income will be

Then the income is given by the function

To find the maximum value of this functions (thus the maximum income) we need to take the derivative of the function,

no we equate the derivative to zero and solve for x.

This means that we have an extreme value of the function when x=9. Now we need to find out if this value is a maximum or a minimum. To do this we need to take the second derivative of the function, then

Since the second derivative is negative in the point x=9, we conclude that this value is a maximum of the function.
With this we conclude that the number of times that they should raise the price to maximize the income is 9. This means that they will raise the price of the newspaper (9)($0.05)=$0.45.
Therefore the price to maximize the income is $0.35+$0.45=$0.80.
Answer:
b=a √3
Step-by-step explanation:
Given that the number of years should be represented with x, the number of fish in the pond after x years should best be represented with f(x). The equation that would best show the given scenario in the problem above is,
f(x) = 500(2^x)
From the given, 500 is used as the initial population of the fish.
Answer:
The answer to your question is the letter A.
Step-by-step explanation:
Data
Center = (2, 3)
radius = 2
Process
1.- Find the equation of the line
(x - h)² + (y - k)² = r²
-Substitution
(x - 2)² + (y - 3)² = 2²
-Simplification
(x - 2)² + (y - 3)² = 4
-Evaluate the points in the equation
A. (4, 3)
(4 - 2)² + (3 - 3)² = 4
2² + 0 = 4
4 = 4 This point lies in the circle
B (-1, 0)
(-1 - 2)² + (0 - 3)² = 4
-3² + (-3)² = 4
9 + 9 = 4 This point is not part of the circle
C. (1, 3)
(1 - 2)² + (3 - 3)² = 4
(-1)² + (0)² = 4
1 = 4 This point is not part of the circle
D. (3, 4)
(3 - 2)² + (4 - 3)² = 4
1² + 1² = 4
2 = 4 This point is not part of the circle