Your company is given $100 to start off, and makes a $50 profit every week afterwards. Write and solve an inequality to find the minimum number of weeks it will take you to have a profit of $375. It will take you at least weeks to make a profit. *Type your whole number answer in the text box given.

It will take 5.5 weeks to make a profit of $375.

Step-by-step explanation:

Given,

Starting amount of company = $100

Profit per week = $50

Profit to make = $375

Let,

w be the number of weeks.

Therefore,

100 + 50w ≥ 375

Subtracting 100 from both sides;

Dividing both sides by 50

It will take 5.5 weeks to make a profit of $375.

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