TWO-VARIABLE DATA: MODELS AND SCATTERPLOTS 1 — Problem-Solving and Data Analysis

Questions in this quiz (10)

1. A scatterplot shows the relationship between weekly revenue and marketing spending for a company over $$10$$ weeks. A line of best fit is drawn through the data. According to the line of best fit, which of the following is the best estimate of the predicted increase in weekly revenue, in thousands of dollars, for every $$200$$ increase in marketing spending?

   • $$0.04$$
   • $$0.8$$
   • $$1.5$$
   • $$3$$

2. The scatterplot shows the relationship between two variables, $$x$$ and $$y$$. The data are well modeled by an exponential function of the form $$y=a(b)^x$$ where $$a$$ and $$b$$ are positive constants. The model passes through the points $$(2,80)$$ and $$(8,1600)$$. Which of the following is closest to the value of $$b$$?

   • $$1.28$$
   • $$1.50$$
   • $$1.65$$
   • $$2.25$$

3. A coach collected data on the number of hours $$h$$ that athletes trained each week and their performance scores $$p$$ on a fitness test. The line of best fit for the data is given by the equation $$p=5h+48$$. For one athlete who trained $$6$$ hours in a week, the score predicted by the line of best fit was $$6$$ points greater than the athlete’s actual score. What was the athlete’s actual score?

   • $$72$$
   • $$75$$
   • $$78$$
   • $$81$$

4. For $$x$$ > $$0$$, the function $$f$$ is defined as follows:$$f(x)$$ is the value obtained by subtracting $$30\%$$ of $$x$$ from $$200$$.Which of the following could describe this function?

   • Decreasing exponential
   • Decreasing linear
   • Increasing exponential
   • Increasing linear

5. Two service plans are offered as shown in the table below. Which of the following is true about the annual increase in cost for the two plans?

   • The annual increase for Plan $$X$$ is always greater than the annual increase for Plan $$Y$$.
   • The annual increase for Plan $$X$$ is always less than the annual increase for Plan $$Y$$.
   • The annual increase for Plan $$X$$ is greater than the annual increase for Plan $$Y$$ at first but eventually is less.
   • The annual increase for Plan $$X$$ is less than the annual increase for Plan $$Y$$ at first but eventually is greater.

6. Two employees receive annual raises as shown in the table below. Employee $$P$$'s raise is compounded annually. Which of the following statements is true about their raises?

   • Employee $$P$$ always receives a higher raise per year than Employee $$Q$$.
   • Employee $$P$$ always receives a lower raise per year than Employee $$Q$$.
   • Employee $$P$$ receives a higher raise per year than Employee $$Q$$ at first but eventually receives a lower raise per year.
   • Employee $$P$$ receives a lower raise per year than Employee $$Q$$ at first but eventually receives a higher raise per year.

7. A botanist is studying the growth of a plant. The data below shows the height, $$h$$, in centimeters, of the plant at the end of several different weeks, $$w$$. The line of best fit for the data is given by the equation $$h=5w+15$$.For the data point that is furthest vertically from the line of best fit, what is the actual height, in centimeters?

   • $$30$$
   • $$45$$
   • $$52$$
   • $$62$$

8. For $$z$$ > $$0$$, the function $$k$$ is defined as follows:$$k(z)$$ is the result of subtracting $$3$$ times $$z$$ from $$50$$.Which of the following could describe this function?

   • Decreasing exponential
   • Decreasing linear
   • Increasing exponential
   • Increasing linear

9. A scatterplot shows the relationship between two variables, $$w$$ and $$h$$. A line of best fit for the data passes through the points $$(2,11)$$ and $$(8,26)$$. Which of the following equations best represents the line of best fit?

   • $$h=1.5w+8$$
   • $$h=2.0w+7$$
   • $$h=2.5w+6$$
   • $$h=3.0w+5$$

10. A market researcher is analyzing the relationship between the price of a product and the number of units sold per week. A line of best fit for the collected data is given by the equation $$u=-12p+850$$, where $$u$$ is the number of units sold and $$p$$ is the price in dollars. For one week, the price was $$30$$ dollars and $$495$$ units were sold. According to the model, the actual number of units sold was how many more than the number predicted by the line of best fit?

    • $$5$$
    • $$10$$
    • $$12$$
    • $$30$$