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2 answers:
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Answer:
Step-by-step explanation:
First determine whether it is a sine function or a cosine function. Since
sin(x) = 0 at x = 0 and we see indeed that the value of the function is 0 at x = 0 it must be a sine function
The general equation of a sine function is
where a is the amplitude. The amplitude is one-half the difference between the lowest and highest values in the graph.From the graph we can see that the highest value is 3/4 and lowest is -3/4 so the amplitude = 1/2 (3/4 + 3/4) = 3/4
If the amplitude were positive, the function would be increasing at (0,0) and going up to its amplitude value. However we can see that the function is decreasing at (0,0 ) and goes down to -3/4. Therefore the amplitude a has a negative sign so a = -3/4
To compute b, note that the period of the function ie where it finishes a full cycle is 3π since the function at that x value repeats itself. The relationship between b and the period is 2π/b = 3π in this particular case
This gives b = 2/3
So a = -3/4, b = 2/3 and the equation is
Answer:
Cost function:
Revenue function
Profit function
Dozens needed for a specific profit P
If 150 dozen cookies are sold the profit is negative, so the business is loosing $322.
Step-by-step explanation:
We can list the costs as:
- Fixed monthly cost, $790/month.
- Variable costs, $0.24/cookie, which are (12*0.24) = $2.88 a dozen.
Then, we can write the cost function C(x) as:
being C(x): the monthly cost and x: the number of dozens produced per month.
The revenue can be calculated as the price ($6 a dozen) multiplied by the number of dozens x:
The profit can be calculated substracting the total cost C(x) from the revenue R(x).
The number of cookies (in dozens) that must be produced and sold for a monthly profit can be calculated from the previous equation for P(x).
For a monthly profit P, the number of dozens that need to be sold are:
If 150 dozen cookies are sold, the profit made is:
The profit is negative, so the business is loosing $322.