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Eagle Eye Tour Company plans to offer scenic helicopter tours as its newest attraction. The company spent $\$979,000$ on a pre-owned helicopter, which is expected to lose about $11\%$ of its value each year. Write an exponential equation in the form $y=a(b)^x$ that can model the value of the helicopter, $y$ , $x$ years after purchase. Use whole numbers, decimals, or simplified fractions for the values of $a$ and $b$ . $y =$ To the nearest hundred dollars, how much will the helicopter be worth $6$ years after purchase?

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Write exponential functions: word problems

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Q. Eagle Eye Tour Company plans to offer scenic helicopter tours as its newest attraction. The company spent

\$979,000

on a pre-owned helicopter, which is expected to lose about

11\%

of its value each year. Write an exponential equation in the form

y=a(b)^x

that can model the value of the helicopter,

y

,

x

years after purchase. Use whole numbers, decimals, or simplified fractions for the values of

a

and

b

.

y =

To the nearest hundred dollars, how much will the helicopter be worth

6

years after purchase?

Find initial value and rate: Find the initial value $a$ and the rate of depreciation $r$ . The initial value $a$ is the cost of the helicopter when it was purchased, which is $\$979,000$ . The rate of depreciation $r$ is $11\%$ per year, which can be expressed as a decimal $0.11$ .
Determine decay factor: Determine the decay factor $b$ . Since the helicopter loses value each year, we subtract the rate of depreciation from $1$ to find the decay factor. $b = 1 - r$ $b = 1 - 0.11$ $b = 0.89$
Write exponential decay equation: Write the exponential decay equation. $\newline$ Using the values of $a$ and $b$ , we can write the equation in the form $y = a(b)^x$ . $\newline$ $y = 979,000(0.89)^x$
Calculate value after $6$ years: Calculate the value of the helicopter $6$ years after purchase. $\newline$ To find the value after $6$ years, we substitute $x$ with $6$ in the equation. $\newline$ $y = 979,000(0.89)^6$
Perform calculation: Perform the calculation. $\newline$ $y = 979,000(0.89)^6$ $\newline$ $y \approx 979,000 \times 0.532$ $\newline$ $y \approx 520,868$ $\newline$ To the nearest hundred dollars, the helicopter will be worth approximately $\$520,900$ after $6$ years.

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