Question

Predicting an Airplane's Height The measured height, in feet, of an airplane at certain times, in minutes, after takeoff can be modeled using the regression equation y=(29,864)/(1+9.381e^(-0.9948x)). To the nearest hundred feet, what is the predicted height of the airplane after 18 minutes? 29864

Answer 1

The predicted height of the airplane after 18 minutes is approximately 28,678 feet.

Step-by-step explanation:

To find the predicted height of the airplane after 18 minutes, we can plug in the value of x = 18 into the regression equation y=(29,864)/(1+9.381e^(-0.9948x)).

So, y = (29,864)/(1+9.381e^(-0.9948*18)).

Calculating this expression, we find that the predicted height of the airplane after 18 minutes is approximately 28,678 feet.

Answer 2

The predicted height of the airplane after 18 minutes using the regression equation is approximately 29,864 feet, rounded to the nearest hundred feet.

The given regression equation is:

`\[ y = (29,864)/(1+9.381e^(-0.9948x)) \]`

Where:

- x represents time in minutes after takeoff.

- y represents the measured height of the airplane in feet.

To find the predicted height of the airplane after 18 minutes, substitute x = 18 into the equation:

`\[ y = (29,864)/(1+9.381e^(-0.9948(18))) \]`

Let's calculate this:

`\[ y \approx (29,864)/(1+9.381e^(-17.9064)) \]`

`\[ y \approx (29,864)/(1+9.381(1.0398 * 10^(-8))) \]`

`\[ y \approx (29,864)/(1+9.751 * 10^(-8)) \]`

Now, compute the predicted height:

`\[ y \approx (29,864)/(1+9.751 * 10^(-8)) \approx (29,864)/(1) \approx 29,864 \text{ feet} \]`

Rounded to the nearest hundred feet, the predicted height of the airplane after 18 minutes is approximately 29,900 feet.