The manager of Gerard's Restaurant is making a supply order for the coming week. Based on his past experience, the manager has constructed a
model which shows that pasta is chosen over salad and enchiladas 62% of the time.
The table below shows the results of three days of business, with breakdowns for how many customers ordered pasta, salad, and enchiladas.
Day Pasta Salad Enchiladas
1 130 37 38
2 175 17 14
10531 33

Classify the results for each category as either consistent or inconsistent with the model.
Consistent with
Model
Inconsistent with
Model

Total of all
3 days results
Day 1 results
Day 2 results
Day 3 results

18.75 gallons

step-by-step explanation:

answer: 80,000

step-by-step explanation:

the population doubles every day.

10,000*2=20,000 day 4

20,000*2=40,000 day 5

40,000*2=80,000 day 6

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

step-by-step explanation: