2. Find a quadratic model for the given data.

{(1, 1), (2, 1), (4, 8), (5, 14), (6, 25)}

3. A graphing calculator is recommended.

The data in the table below show the distance, in feet, a ball travels for various swing speeds, in miles per hour, of a bat.

Bat speed (mph)	Distance (ft)
40	201
45	213
50	240
60	270
70	294
75	325
80	330

(a) Find the linear regression equation for these data. (Round all numerical values to three decimal places.)

y =

(b) Using the regression model, what is the expected distance a ball will travel when the bat speed is 58 miles per hour? Round to the nearest foot.

---------- ft

4. The temperature at various times on a summer day at a resort in southern California is given in the following table. The variable t is the number of minutes after 6:00 A.M., and the variable T is the temperature in degrees Fahrenheit.

t (min)	T (F)
20	57
40	68
80	70
120	76
160	80
200	80
240	87
280	87
320	87
360	87
400	79

(a) Find a quadratic model for these data. (Round all numerical values to five decimal places.) T =

(b) Use the model to predict the temperature at 1:00 P.M. Round to the nearest tenth of a degree. -------- F

5. The survival of certain larvae after hatching depends on the temperature (in degrees Celsius) of the surrounding environment. The following table shows the number of larvae that survive at various temperatures. Find a quadratic model for these data.

Larvae Surviving for Various Temperatures

Temp. (C)	Number Surviving
20	40
21	47
22	52
23	61
24	64
25	64
26	68
27	67
28	64
29	62
30	61