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Eagle Eye Tour Company plans to offer scenic helicopter tours as its newest attraction. The company spent $979,000\$979,000 on a pre-owned helicopter, which is expected to lose about 11%11\% of its value each year. Write an exponential equation in the form y=a(b)xy=a(b)^x that can model the value of the helicopter, yy, xx years after purchase. Use whole numbers, decimals, or simplified fractions for the values of aa and bb. y=y = To the nearest hundred dollars, how much will the helicopter be worth 66 years after purchase?

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Q. Eagle Eye Tour Company plans to offer scenic helicopter tours as its newest attraction. The company spent $979,000\$979,000 on a pre-owned helicopter, which is expected to lose about 11%11\% of its value each year. Write an exponential equation in the form y=a(b)xy=a(b)^x that can model the value of the helicopter, yy, xx years after purchase. Use whole numbers, decimals, or simplified fractions for the values of aa and bb. y=y = To the nearest hundred dollars, how much will the helicopter be worth 66 years after purchase?
  1. Find initial value and rate: Find the initial value aa and the rate of depreciation rr. The initial value aa is the cost of the helicopter when it was purchased, which is $979,000\$979,000. The rate of depreciation rr is 11%11\% per year, which can be expressed as a decimal 0.110.11.
  2. Determine decay factor: Determine the decay factor bb. Since the helicopter loses value each year, we subtract the rate of depreciation from 11 to find the decay factor. b=1−rb = 1 - r b=1−0.11b = 1 - 0.11 b=0.89b = 0.89
  3. Write exponential decay equation: Write the exponential decay equation.\newlineUsing the values of aa and bb, we can write the equation in the form y=a(b)xy = a(b)^x.\newliney=979,000(0.89)xy = 979,000(0.89)^x
  4. Calculate value after 66 years: Calculate the value of the helicopter 66 years after purchase.\newlineTo find the value after 66 years, we substitute xx with 66 in the equation.\newliney=979,000(0.89)6y = 979,000(0.89)^6
  5. Perform calculation: Perform the calculation.\newliney=979,000(0.89)6y = 979,000(0.89)^6\newliney≈979,000×0.532y \approx 979,000 \times 0.532\newliney≈520,868y \approx 520,868\newlineTo the nearest hundred dollars, the helicopter will be worth approximately $520,900\$520,900 after 66 years.

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