A Clothing Shop opened eight years ago. The first year it made $5000 profit. Each year
thereafter the profits averaged 36% greater than the previous year. How much profit would be earned in the 14th year if this trend continues? Round to two decimal places.
help!
500 * 1.36^14 =_____
where did you get 500 from?
To find the profit in the 14th year, we need to calculate the percentage increase for each year and then apply it to the previous year's profit.
Let's calculate the average annual increase:
Year 1: $5000 profit
Year 2: 36% increase = $5000 + ($5000 * 0.36) = $6800 profit
Year 3: 36% increase = $6800 + ($6800 * 0.36) = $9256 profit
Year 4: 36% increase = $9256 + ($9256 * 0.36) = $12595.16 profit
Year 5: 36% increase = $12595.16 + ($12595.16 * 0.36) = $17135.23 profit
Year 6: 36% increase = $17135.23 + ($17135.23 * 0.36) = $23312.91 profit
Year 7: 36% increase = $23312.91 + ($23312.91 * 0.36) = $31725.83 profit
Year 8: 36% increase = $31725.83 + ($31725.83 * 0.36) = $43194.51 profit
Now that we have the pattern, we can continue to calculate the profits for the following years:
Year 9: 36% increase = $43194.51 + ($43194.51 * 0.36) = $58787.08 profit
Year 10: 36% increase = $58787.08 + ($58787.08 * 0.36) = $80032.77 profit
Year 11: 36% increase = $80032.77 + ($80032.77 * 0.36) = $108870.94 profit
Year 12: 36% increase = $108870.94 + ($108870.94 * 0.36) = $148397.58 profit
Year 13: 36% increase = $148397.58 + ($148397.58 * 0.36) = $201736.67 profit
Year 14: 36% increase = $201736.67 + ($201736.67 * 0.36) = $274663.10 profit
Therefore, if the trend continues, the profit in the 14th year would be $274,663.10.