The table shows the heightsh (in feet) of a sponge t seconds after it was dropped by a window cleaner on to Time, t 1 1.5 2.5 3 Height, h 280 264 244 180 136 a. Use a graphing calculator to create a scatter plot. Which better represents the data, a line or a parabola? Expla A parabola best represents the data because there is not a constant rate of change. b. Use the regression feature of your calculator to find the model that best fits the data. The model is h = c. Use the model in part (b) to predict when the sponge will hit the ground. Round your answer to the nearest hundredth. about 4.18 v seconds

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Algebra 2 

chapter 2: Modeling with Quadratic Functions > Section 2.4 Exercise 27 

b. Use the regression feature of your calculator to find the model that best fits the data?

The model is h =

**Table: Heights of a Sponge Over Time**

The table presents the heights \( h \) (in feet) of a sponge at various times \( t \) (in seconds) after being dropped by a window cleaner.

| Time, \( t \) (seconds) | Height, \( h \) (feet) |
|-------------------------|-------------------------|
| 0                       | 280                     |
| 1                       | 264                     |
| 1.5                     | 244                     |
| 2.5                     | 180                     |
| 3                       | 136                     |

**a. Scatter Plot Analysis**

Use a graphing calculator to create a scatter plot of the data. Determine whether a line or a parabola better represents the data by examining the rate of change. A parabola best represents the data because there is not a constant rate of change.

**b. Regression Model**

Utilize the regression feature of your calculator to find the mathematical model that best fits the given data. 
The model is \( h = \_\_\_ \).

**c. Prediction Using the Model**

Apply the model from part (b) to predict the time when the sponge will hit the ground. Round the prediction to the nearest hundredth.
The sponge will hit the ground in about 4.18 seconds.

**d. Domain and Range Interpretation**

Identify and interpret the domain and range pertinent to this scenario.
Transcribed Image Text:**Table: Heights of a Sponge Over Time** The table presents the heights \( h \) (in feet) of a sponge at various times \( t \) (in seconds) after being dropped by a window cleaner. | Time, \( t \) (seconds) | Height, \( h \) (feet) | |-------------------------|-------------------------| | 0 | 280 | | 1 | 264 | | 1.5 | 244 | | 2.5 | 180 | | 3 | 136 | **a. Scatter Plot Analysis** Use a graphing calculator to create a scatter plot of the data. Determine whether a line or a parabola better represents the data by examining the rate of change. A parabola best represents the data because there is not a constant rate of change. **b. Regression Model** Utilize the regression feature of your calculator to find the mathematical model that best fits the given data. The model is \( h = \_\_\_ \). **c. Prediction Using the Model** Apply the model from part (b) to predict the time when the sponge will hit the ground. Round the prediction to the nearest hundredth. The sponge will hit the ground in about 4.18 seconds. **d. Domain and Range Interpretation** Identify and interpret the domain and range pertinent to this scenario.
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