2.5B & 2.6 Review

2.5B & 2.6 Review

By Cayley Garrison

Multiple Choice

A tractor that costs $150,000 depreciates in value, v, by 5.4% per year, t. Which function models this scenario?

• $$v\left(t\right)=150000\left(0.946\right)^t$$

• $$v\left(t\right)=150000\left(0.054\right)^t$$

• $$v\left(t\right)=150000\left(1.054\right)^t$$

• $$v\left(t\right)=150000\left(1.946\right)^t$$

Multiple Choice

A baseball card is worth $50 and its value, v, appreciates at a rate of 23.5% per year, t. Which function models this scenario?

• $$v\left(t\right)=50\left(0.235\right)^t$$

• $$v\left(t\right)=50\left(0.765\right)^t$$

• $$v\left(t\right)=50\left(1.235\right)^t$$

• $$v\left(t\right)=50\left(1.765\right)^t$$

Multiple Choice

A plague of mice has hit! Starting with only 30 mice, their population, p, increases by 650% every month, m. Which function models this scenario?

• $$p\left(m\right)=30\left(6.5\right)^m$$

• $$p\left(m\right)=30\left(3.5\right)^m$$

• $$p\left(m\right)=30\left(4.5\right)^m$$

• $$p\left(m\right)=30\left(7.5\right)^m$$

Multiple Choice

700 grams of radioactive material, m, decays at a rate of 2.4% per year, t. Which function models this scenario?

• $$m\left(t\right)=700\left(0.024\right)^t$$

• $$m\left(t\right)=700\left(0.976\right)^t$$

• $$m\left(t\right)=700\left(1.024\right)^t$$

• $$m\left(t\right)=700\left(1.976\right)^t$$

Half-Life and Doubling Time

Multiple Choice

A population, p, of 500 people doubles every 35 years, t. Which function models the scenario?

• $$p\left(t\right)=500\left(2\right)^{\frac{t}{2}}$$

• $$p\left(t\right)=500\left(35\right)^{\frac{t}{2}}$$

• $$p\left(t\right)=500\left(2\right)^{\frac{t}{35}}$$

• $$p\left(t\right)=500\left(2\right)^{35t}$$

Multiple Choice

There is 500 grams, g, of radioactive material. It's Half-Life is 5,700 years, t. Which function models the scenario?

• $$p\left(t\right)=500\left(\frac{1}{2}\right)^{\frac{t}{2}}$$

• $$p\left(t\right)=500\left(5700\right)^{\frac{t}{2}}$$

• $$p\left(t\right)=500\left(\frac{1}{2}\right)^{\frac{t}{5700}}$$

• $$p\left(t\right)=500\left(\frac{1}{2}\right)^{5700t}$$

Residual Plots

Multiple Choice

A student creates a model for a data set. The residual plot for their exponential regression is shown. Is the model appropriate? Why or why not?

• The exponential model is not appropriate because there is a clear pattern in the graph of the residuals.

• The exponential model is not appropriate because there is no clear pattern in the graph of the residuals

•  The exponential model is appropriate because there is a clear pattern in the graph of the residuals.

•  The exponential model is appropriate because there is no clear pattern in the graph of the residuals.

Multiple Choice

A student creates a model for a data set. The residual plot for their quadratic regression is shown. Is the model appropriate? Why or why not?

• The quadratic model is not appropriate because there is a clear pattern in the graph of the residuals.

• The quadratic model is not appropriate because there is no clear pattern in the graph of the residuals

•  The quadratic model is appropriate because there is a clear pattern in the graph of the residuals.

•  The quadratic model is appropriate because there is no clear pattern in the graph of the residuals.

Over & Under Estimates

Multiple Choice

The heights of fathers and sons are being compared. A regression model was calculated with the fathers height (in inches) as input values and the sons height (in inches) as the output values. The residual plot for the regression model and data points is shown. The point P has the coordinate (68, 2.784). What does the point P indicate in the context?

• Since the point is above the x-axis, for the father with a height of 68in, the model underestimates the sons height by 2.784in

• Since the point is above the x-axis, for the father with a height of 68in, the model overestimates the sons height by 2.784in

• Since the point is above the x-axis, for the son with a height of 68in, the model underestimates the fathers height by 2.784in

• Since the point is above the x-axis, for the son with a height of 68in, the model overestimates the fathers height by 2.784in

Multiple Choice

The heights of fathers and sons are being compared. A regression model was calculated with the fathers height (in inches) as input values and the sons height (in inches) as the output values. The residual plot for the regression model and data points is shown. The point Q has the coordinate (76, -3.01). What does the point P indicate in the context?

• Since the point is below the x-axis, for the father with a height of 76in, the model underestimates the sons height by 3.01in

• Since the point is below the x-axis, for the father with a height of 76in, the model overestimates the sons height by 3.01in

• Since the point is below the x-axis, for the son with a height of 76in, the model underestimates the fathers height by 3.01in

• Since the point is below the x-axis, for the son with a height of 76in, the model overestimates the fathers height by 3.01in

Multiple Choice

The grades of students taking AP Stats and AP Pre-Calc are collected and compared. A regression model was calculated with the AP Stats grade as input values and AP Pre-Calc grade as the output values. The residual plot for the regression model and data points is shown. The point P has the coordinate (97, 12.04). What does the point P indicate in the context?

• Since the point is above the x-axis, for the AP Pre-Calc grade of 97, the model underestimates the AP Stats grade by 12.04

• Since the point is above the x-axis, for the AP Pre-Calc grade of 97, the model overestimates the AP Stats grade by 12.04

• Since the point is above the x-axis, for the AP Stats grade of 97, the model underestimates the AP Pre-Calc grade by 12.04

• Since the point is above the x-axis, for the AP Stats grade of 97, the model overestimates the AP Pre-Calc grade by 12.04

Multiple Choice

The grades of students taking AP Stats and AP Pre-Calc are collected and compared. A regression model was calculated with the AP Stats grade as input values and AP Pre-Calc grade as the output values. The residual plot for the regression model and data points is shown. The point Q has the coordinate (82, -7.85). What does the point P indicate in the context?

• Since the point is below the x-axis, for the AP Pre-Calc grade of 82, the model underestimates the AP Stats grade by 7.85

• Since the point is below the x-axis, for the AP Pre-Calc grade of 82, the model overestimates the AP Stats grade by 7.85

• Since the point is below the x-axis, for the AP Stats grade of 82, the model underestimates the AP Pre-Calc grade by 7.85

• Since the point is below the x-axis, for the AP Stats grade of 82, the model overestimates the AP Pre-Calc grade by 7.85