Deanna runs a bakery that sells gourmet doughnuts. At $5 per doughnut she sells 100 doughnuts in a day. Her daily costs to make the doughnuts are $175. Deanna estimates that for each $0.50 decrease in cost she will sell
35 more doughnuts each day. The daily profits for the doughnuts can be modeled with the equation:
P(x) = (100+35x)(5 -0.5x) -175, where x represents the number of $0.50 decreases in price. Use
technology to graph the profit equation and determine the price per doughnut that Deanna should charge to
maximize her profits.

$3.21

Step-by-step explanation:

This question asks for use of technology, so you can use a hand graphing calculator or the desmos website (which I used).

I have attached the screenshot of this graph. We want the maximum value on the y axis (the axis representing profit). We can see that the highest point is at (3.571, 548.214), so this is when she makes the most money.

This means that she makes the most profit at 3.571 50 cent decreases.

3.571×0.5 is a decrease by $1.7855.

This means the best price is 5-1.7855, which is 3.2145. This can be rounded to $3.21

h= 12 inches

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt