Respuesta :
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
The money she will make in all over 4 weeks would be $238.705.
What is the formula for compound interest profit?
Lucy finds that each week during the summer her profits increase by 10% over what they were the previous week, we can find her profit using the formula for compound interest which is given below:
[tex]profit(n) = profit(1)\times (1 + r)^{n-1}[/tex]
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 grow and n is the number of weeks.
[tex]profit(1) = 50\\\\profit(2) = 50\times (1.1)^{2-1} = 55\\profit(3) = 50\times (1.1)^{3-1} = 60.5\\profit(4) = 50\times (1.1)^{4-1} = 73.205[/tex]
Her total profit over 4 weeks was:
The total profit = profit(1) + profit(2) + profit(3) + profit(4)
The total profit = 50 + 55 + 60.5 + 73.20
= 238.705
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