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MTH 215 Week 4 MyMathLab® Study Plan for Week 4 Checkpoint

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• 8.A Growth: Linear versus Exponential

• Decide if a statement involving linear and exponential growth makes sense.
• Distinguish between linear and exponential growth or decay.
• Solve applications involving linear and exponential growth.

• 9.A Functions: The Building Blocks of Mathematical Models

• Determine if two variables are related in a way that can be described as a function.
• Describe the relationship between two variables.
• Graph and describe functions.

• 9.B Linear Modeling

• Decide if a statement involving linear models makes sense.
• Analyze characteristics of linear graphs.
• Solve applications involving linear functions.
• Graph linear equations.

• 9.C Exponential Modeling

• Decide if a statement involving exponential models makes sense.
• Brief Review – Logarithms
• Solve applications of exponential growth and decay.

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning.

Money in a bank account earning compound interest at an annual percentage rate of​ 3% is an example of exponential growth.

Choose the correct answer below.

A.

The statement does not makes sense because the money in the account grows by the same absolute​ amount, which is an example of linear growth.

B.

The statement makes sense because the money in the account grows by the same​ percentage, which is an example of exponential growth.

C.

The statement makes sense because the money in the account grows by the same absolute​ amount, which is an example of exponential growth.

D.

The statement does not make sense because the money in the account grows by the same​ percentage, which is an example of linear growth.

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of​ wheat, on the third​ square, four grains of​ wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining​ squares, how many grains of wheat should be placed on square 16​? Also find the total number of grains of wheat on the board at this time and their total weight in pounds.​ (Assume that each grain of wheat weighs​ 1/7000 pound.)

How many grains of wheat should be placed on square 16​?

32768 grains

How many total grains of wheat should be on the board after the the grains of wheat have been placed on square 16​?

65535 grains

What is the total weight of all the grains of wheat on the board after the grains of wheat have been placed on square 16​?

9.4 pounds

​(Round to the nearest tenth as​ needed.)

In the following​ situation, state whether two variables are related in a way that might be described by a function. If​ so, identify the independent and dependent variables.

You walk through a used car lotwalk through a used car lot and list the price and model year of each car you see.

Determine whether the two variables are related in a way that might be described by a function. If the situation could be described as a​ function, then identify the independent and dependent variables. Choose the correct answer below.

A.

The situation cannot be described by a function.

B.

The situation cancan be described by a function. The dependent variable is theThe dependent variable is the price and the independent variable is the model.price and the independent variable is the model.

C.

The situation can be described by a function. There is a dependent​ variable, but no independent variable. The dependent variable is thethe priceprice.

D.

The situation can be described by a function. The dependent variable is the modelmodel and the independent variable is the price.is the price. nothing

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning.

I graphed two linear​ functions, and the one with the greater rate of change had the greater slope.

Choose the correct answer below.

A.

This makes sense. According to the definition of linear​ functions, the rate of change is equal to the slope of the graph and the greater the rate of​ change, the greater the slope.

B.

This does not make sense. According to the definition of linear​ functions, the slope of all linear functions must be the same.

C.

This does not make sense. According to the definition of linear​ functions, the initial value is equal to the slope of the graph.​ Thus, the rate of change does not relate to the slope.

D.

This makes sense. According to the definition of linear​ functions, the initial value is equal to the slope of the graph.​ Thus, the rate of change does not relate to the slope.

Consider the graph to the right.

1. In​ words, describe the function shown on the graph.

b.Find the slope of the graph and express it as a rate of change.

1. Briefly discuss the conditions under which a linear function is a realistic model for the given situation.

A graph has a horizontal axis labeled Time (hours) from 0 to 5 in increments of 1 and a vertical axis labeled Rain Depth (inches) from 0 to 5 in increments of 1. A line that rises from left to right passes through the points (0, 0) and (4, 1).

1. Select the correct answer below.

A.

According to the​ function, the rain depth decreases by 11 inchinch every 44 hourshours.

B.

According to the​ function, the rain depth decreases by 44 inchesinches every 11 hourhour.

C.

According to the​ function, the rain depth increases by 1 inchinch every 4 hourshours.

D.

According to the​ function, the rain depth increases by 44 inchesinches every 11 hourhour.

1. Calculate the slope and represent it as a rate of change.

rate of changeequals=

one fourth

inch(es) per hour

​(Type an integer or a​ fraction.)

1. Select the correct answer below.

A.

It is a good model if the rainfall is constant for four hours.

B.

It is a good model if the rainfall is changing for two​ hours, then constant for two hours.

C.

It is a good model if the rainfall is not constant four hours.

D.

It is a good model if the rainfall is constant for two hours and then changing for two hours.

The following situation involves a rate of change that is constant. Write a statement that describes how one variable changes with respect to the​ other, give the rate of change numerically​ (with units), and use the rate of change rule to answer any questions.

Snow accumulates during a storm at a constant rate of 2.7 inches per hour. How much snow accumulates in the first 5.1 ​hours? in the first 9.8 ​hours?

Which statement describes this​ situation?

A.

The snow accumulated varies with respect to time with a rate of change of 2.72.7 ​h/in.

B.

Time varies with respect to the snow accumulated with a rate of change of 2.72.7 ​in/h.

C.

Time varies with respect to the snow accumulated with a rate of change of 2.72.7 ​h/in.

D.

The snow accumulated varies with respect to time with a rate of change of 2.7 ​in/h.

How much snow has accumulated after the first 5.1 ​hours?

13.77 inches

​(Type an integer or a​ decimal.)

How much snow has accumulated after the first 9.8 ​hours?

26.46 inches

​(Type an integer or a​ decimal.)

Give the slope and​ y-intercept of the line whose equation is given below. Then graph the linear function.

y equals negative 2 x plus 1    y=−2x+1

The slope of the line is

−2

​(Simplify your​ answer.)

The​ y-intercept is

1

​(Type an integer or a simplified​ fraction.)

Use the graphing tool to graph the linear equation. Use the slope and​ y-intercept when drawing the line.

Solve for x.

2 Superscript x equals=32

The solution is xequals=

5

​(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as​ needed.)

Consider the following case of exponential growth. Complete parts a through c below.

The population of a town with an initial population of

71,000 grows at a rate of 3.5​% per year.

1. Create an exponential function of the form

Q=Q0×(1+r)t​,

​ (where r >0 for growth and r <0 for​ decay) to model the situation described.

Q=71000×​(1.035​) t

​(Type integers or​ decimals.)

1. Create a table showing the value of the quantity Q for the first 10 years of growth.

​(Round to the nearest whole number as​ needed.)

1. Make a graph of the exponential function. Choose the correct graph below.

A.

A coordinate system has a horizontal axis labeled Year from 0 to 10 in increments of 1 and a vertical axis labeled Population from 70000 to 110000 in increments of 10000. A curve rises from left to right at an increasing rate, passing through the points (0,71,000) and (5,84000). All coordinates are approximate.

B.

A coordinate system has a horizontal axis labeled Year from 0 to 10 in increments of 1 and a vertical axis labeled Population from 70000 to 120000 in increments of 10000. A curve rises from left to right at a decreasing rate, passing through the points (0,89000) and (5,101000). All coordinates are approximate.

C.

A coordinate system has a horizontal axis labeled Year from 0 to 10 in increments of 1 and a vertical axis labeled Population from 60000 to 110000 in increments of 10000. A curve falls from left to right at a decreasing rate, passing through the points (0,93000) and (5,82000). All coordinates are approximate.

D.

A coordinate system has a horizontal axis labeled Year from 0 to 10 in increments of 1 and a vertical axis labeled Population from 20000 to 110000 in increments of 10000. A curve falls from left to right at an increasing rate, passing through the points (0,83000) and (5,70000). All coordinates are approximate.

Question is complete.

Between 2005 and 2008​, the average rate of inflation was about 3.8​% per year. If a cart of groceries cost ​$150 in​ 2005, what did it cost in 2008​?

A cart of groceries cost approximately ​$

167.76

in 2008

​(Round to two decimal places as​ needed.)