Question

Lucy's lemonade stand has increasing profits each week during the hot summer months. Lucy finds that each week during the summer her profits increase by 10% over what they were the previous week. In her first week of business, her profits were $50. How much money will she make in all over 4 weeks?

Answer 1

Answer:

Lucy's profit over 4 weeks was $238.705

Step-by-step explanation:

Since the value of Lucy's profit increase by 10% over what they were on the previous week, we can model her profit using the formula for compounded interest which is given below:

profit(n) = profit(1)*(1 + r)^(n-1)

Where profit(n) is the profit on the nth week, profit(0) is the profit on the initial week, r is the rate at which her profits grows and n is the number of weeks. Applying the data from the problem, we have:

profit(1) = 50

profit(2) = 50*(1.1)^(2-1) = 55

profit(3) = 50*(1.1)^(3-1) = 60.5

profit(4) = 50*(1.1)^(4-1)  = 73.205

Her total profit over 4 weeks was:

total profit = profit(1) + profit(2) + profit(3) + profit(4)

total profit = 50 + 55 + 60.5 + 73.20 = 238.705