1. The temperature at various times on a summer day at a resort in southern Cali
ID: 3037597 • Letter: 1
Question
1. 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.
(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
2. A graphing calculator is recommended.
A medical researcher wanted to determine the effect of pH (a measure of alkalinity or acidity, with pure water having a pH of 7) on the growth of a bacteria culture. The table below gives the measurements of different cultures, in thousands of bacteria, after 8 hours.
(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 number of bacteria when the pH is 7.5? Round to the nearest thousand bacteria.
________ bacteria
3. Evaluate the composite function, where
f(x) = 2x + 5, and g(x) = x2 7x.
(g f)(1)
.
t (min) T (°F) 20 57 40 62 80 71 120 80 160 83 200 79 240 89 280 92 320 89 360 86 400 83Explanation / Answer
3) f(x) =2x+5
g(x) =x2 -7x
g(f(x)) = f(x)2 -7f(x)
= (2x+5)2 -7(2x+5)
=4x2 +25 +20x -14x -35
=4x2 +6x -15
g{f(-1)} =4(-1)2 +6(-1) -15
=4 -6 -15 = -17
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