Question
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? $
Answers
Answered by
GPT-4o mini
To model the value of the helicopter over time, we can use the exponential decay formula in the form \(y = a(b)^x\).
1. **Determine \(a\)**: This is the initial value of the helicopter, which is given as $979,000. So, \(a = 979000\).
2. **Determine \(b\)**: Since the helicopter is expected to lose about 11% of its value each year, this means it retains 89% of its value. Therefore, \(b = 1 - 0.11 = 0.89\).
3. **Formulate the exponential equation**: Now we can write the equation as:
\[
y = 979000(0.89)^x
\]
4. **Calculate the value of the helicopter after 6 years**: We substitute \(x = 6\) into the equation:
\[
y = 979000(0.89)^6
\]
First, calculate \((0.89)^6\):
\[
(0.89)^6 \approx 0.5277 \quad (\text{using a calculator})
\]
Now, substitute this back into the equation:
\[
y \approx 979000 \times 0.5277
\]
\[
y \approx 517,199.3
\]
5. **Round to the nearest hundred dollars**:
The value of the helicopter after 6 years is approximately \(517,199.3\) dollars, which rounds to **$517,200**.
Thus, the value of the helicopter 6 years after purchase will be approximately **$517,200**.
1. **Determine \(a\)**: This is the initial value of the helicopter, which is given as $979,000. So, \(a = 979000\).
2. **Determine \(b\)**: Since the helicopter is expected to lose about 11% of its value each year, this means it retains 89% of its value. Therefore, \(b = 1 - 0.11 = 0.89\).
3. **Formulate the exponential equation**: Now we can write the equation as:
\[
y = 979000(0.89)^x
\]
4. **Calculate the value of the helicopter after 6 years**: We substitute \(x = 6\) into the equation:
\[
y = 979000(0.89)^6
\]
First, calculate \((0.89)^6\):
\[
(0.89)^6 \approx 0.5277 \quad (\text{using a calculator})
\]
Now, substitute this back into the equation:
\[
y \approx 979000 \times 0.5277
\]
\[
y \approx 517,199.3
\]
5. **Round to the nearest hundred dollars**:
The value of the helicopter after 6 years is approximately \(517,199.3\) dollars, which rounds to **$517,200**.
Thus, the value of the helicopter 6 years after purchase will be approximately **$517,200**.