线性建模・解释与预测

\( s=40+3t \) 
The equation gives the speed s, in miles per hour, of a certain car t seconds after it began to accelerate. What is the speed, in miles per hour, of the car 5 seconds after it began to accelerate?

Caleb used juice to make popsicles. The function \( f\left(x\right)=-5x+30 \) approximates the volume, in fluid ounces, of juice Caleb had remaining after making x popsicles. Which statement is the best interpretation of the y-intercept of the graph of \( y=f\left(x\right) \) in the xy-plane in this context?

A certain open star cluster contains M-type stars and K-type stars. The estimated total mass of M-type and K-type stars in this open star cluster is 127,882 quettagrams. The graph shown models the possible combinations of the number of M-type stars, x, and K-type stars, y, that could be in this open star cluster if all the M-type stars have the same estimated mass and all the K-type stars have the same estimated mass. Based on the graph, which of the following is closest to the estimated mass, in quettagrams, of each M-type star in this cluster?

The graph shows the estimated boiling point  , in degrees Celsius, of a normal paraffin with a molecular weight of x grams per mole, where \( 1\le x\le280 \). Which statement is the best interpretation of the point (149.02, 186.05)?

5G ＋45R = 380
At a school fair, students can win colored tokens that are worth a different number of points depending on the color. One student won G green tokens and R red tokens worth a total of 380 points.The given equation represents this situation.How many more points is a red token worth than a green token?

The graph represents the total charge, in dollars, by an electrician for x hours of work. The electrician charges a onetime fee plus an hourly rate. What is the best interpretation of the slope of the graph?

A neighborhood consists of a 2-hectare park and a 35-hectare residential area. The total number of trees in the neighborhood is 3,934.The equation 2x ＋35y = 3,934 represents this situation. Which of the following is the best interpretation of x in this context?

Keenan made 32 cups of vegetable broth.Keenan then filled x small jars and y large jars with all the vegetable broth he made.The equation 3x ＋5y = 32 represents this situation. Which is the best interpretation of 5y in this context?

F(x)=
(x - 273.15) + 32
The function F gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of x kelvins.If a temperature increased by 2.10 kelvins, by how much did the temperature increase, in degrees Fahrenheit?

Caleb used juice to make popsicles.The function f(x) = -5x ＋30 approximates the volume, in fluid ounces, of juice Caleb had remaining after making x popsicles. Which statement is the best interpretation of the y-intercept of the graph of y = f(x) in the xy-plane in this context?

w(t)= 300- 4t
The function w models the volume of liquid, in milliliters, in a container t seconds after it begins draining from a hole at the bottom. According to the model, what is the predicted volume, in milliliters, draining from the container each second?

A bus is traveling at a constant speed along a straight portion of road. The equation d = 30t gives the distance d, in feet from a road marker, that the bus will be t seconds after passing the marker. How many feet from the marker will the bus be 2 seconds after passing the marker?