carlas clothing shop opened eight years ago. the first year she made $3,000 profit. each year thereafter her profits were about 50% greater than the previous year. how much profit did carla earn during the 18th year of business?
It is a geometric series where
profit for the nth year is given by
p(n)=ar^(n-1)
a=profit of the first year (3000)
r=increment ratio (1.5)
so for the 18th year, profit is
p(18)=3000*1.5^(18-1)
=...
To calculate the profit earned during the 18th year of business, we need to determine the pattern of increasing profits each year.
Given that Carla's profits were about 50% greater than the previous year, we can use that information to calculate the profit for each following year.
Let's break down the calculation step by step:
Year 1: Profit = $3,000
Year 2: Profit = $3,000 + 50% of $3,000
Year 3: Profit = (Year 2 profit) + 50% of (Year 2 profit)
Year 4: Profit = (Year 3 profit) + 50% of (Year 3 profit)
...
Year n: Profit = (Year n-1 profit) + 50% of (Year n-1 profit)
Now, let's calculate the profit for each year up to the 18th year:
Year 1: Profit = $3,000
Year 2: Profit = $3,000 + 50% of $3,000 = $3,000 + $1,500 = $4,500
Year 3: Profit = $4,500 + 50% of $4,500 = $4,500 + $2,250 = $6,750
Year 4: Profit = $6,750 + 50% of $6,750 = $6,750 + $3,375 = $10,125
...
Year 17: We calculate the profit for each year until we reach the 17th year.
Finally, we calculate the profit for the 18th year:
Year 18: Profit = (Year 17 profit) + 50% of (Year 17 profit)
Using the above pattern, we can calculate the profit for the 18th year. However, since we don't have the profit for the 17th year, we cannot provide the exact amount of profit for the 18th year without additional information.