线性建模・解释与预测

The graph shows the possible combinations of the number of pounds of tangerines and lemons that could be purchased for $18 at a certain store. If Melvin purchased lemons and 4 pounds of tangerines for a total of $18, how many pounds of lemons did he purchase?

A linear model estimates the population of a city from 1991 to 2015. The model estimates the population was 57 thousand in 1991, 224 thousand in 2011, and x thousand in 2015. To the nearest whole number, what is the value of x?

The graph shown models the number of residents of a certain city x years after 2010. How many residents does this model estimate the city had in 2010?

As part of a science project on evaporation, Amaya measured the height of a liquid in a container over a period of time. The function \( f\left(x\right)=33-0.18x \)  gives the estimated height, in centimeters (cm), of the liquid in the container x days after the start of the project. Which of the following is the best interpretation of 33 in this context?

A model predicts that a certain animal weighed 241 pounds when it was born and that the animal gained 3 pounds per day in its first year of life. This model is defined by an equation in the form f(x) = a + bx , where f(x)  is the predicted weight, in pounds, of the animal x days after it was born, and a and b are constants. What is the value of a ?

A rectangle has a length that is 15 times its width. The function y =(15w)(w) represents this situation, where y is the area, in square feet, of the rectangle and y>0. Which of the following is the best interpretation of 15w in this context?

\( d=16-\frac{x}{30} \) 
The equation shown gives the estimated amount of diesel d, in gallons, that remains in the gas tank of a truck after being driven x miles, where\( 0\le x\le480 \). What is the estimated amount of diesel, in gallons, that remains in the gas tank of the truck when x = 300?

The graph gives the estimated population y, in thousands, of a town x years since 2003, where \( 0\le x\le5 \) . Which of the following best describes the increase in the estimated population from x = 0 to x = 1?

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?

s =40+3tThe 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?

g(m) = −0.05m + 12.1The given function g models the number of gallons of gasoline that remains from a full gas tank in a car after driving m miles. According to the model, about how many gallons of gasoline are used to drive each mile?

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?