HW6: Mixed Models (2-day)

Instructions

You can find online regression calculators at this site in the fourth column.

To compare exponential and linear growth, check out this video.
For some more exponential growth/decay word problems, check out this video.
For even more exponential word problems, check out this video, this video, and the ones in the sidebar.
For an example of a logarithmic scale, check out this video.

Before you panic about the number of questions... There are three graphing problems after #18. So there's really about 20 questions.

1

Categorize each situation by the type of function that would be the best model. You may use the internet as a resource

The amount of a radioactive material after some time decaying
The cases of a virus after some time spreading
The total earnings collected after some time working at a certain wage
The amount of gas left in a tank after some miles driving
A scale describing the intensity of earthquakes
The value of a car after some years depreciating
The value of a savings account after some years collecting interest
The height of a ball after some time launched from a cannon

Linear
Quadratic
Exponential Growth
Exponential Decay
Logarithmic

1

Categorize the situations according to the model best suited for them. Feel free to look up some equations.

a rating of intensity of an acid based on the concentration of ions
the value of a savings account after some time collecting interest
the distance of a car from the starting line after some time assuming constant acceleration
the amount of candy in my classroom after some number of days (assuming I give roughly the same number of treats each day)
the temperature of a cake after some time being pulled out of the hot oven
the acceleration felt in a car taking a turn at some speed
the number of zombies some time after the first outbreak
a rating of intensity of a sound according to human perception

Linear
Quadratic
Exponential Growth
Exponential Decay
Logarithmic

1

Put the following functions in decreasing order based on their values as x \rightarrow \infty

Hint: It may help to graph in Desmos and zoom out.

f(x) = 222x^{3}
f(x) = (\frac{3}{4})^{3x}
f(x) = (\frac{4}{3})^{2x}
f(x) = 222x^{2}
f(x) = (\frac{4}{3})^{-2x}
f(x) = (\frac{4}{3})^{\frac{1}{2}x}
f(x) = 22x^{2}

The table shows the value of a car during certain years.  Using an expoential model, write an equation for the curve of best fit, then estimate the value of the car in 2016 (x=8).

1

What is the value of growth/decay rate, as a percent?

Enter your answer as an integer.

1

What is the value of the car in 2016, in dollars?

Use four decimal places for the base.

Enter your answer as a number rounded to two decimal places. For example, if your answer were $12.366, you would enter "12.37".

The table below shows the weights of five females of the same height (5'5") along with their body mass index, BMI.  Using a logarithmic model, write an equation for the curve of best fit, then estimate the BMI of a female that weighs 130 pounds.

1

According to your model, what is the BMI of a female that weighs 130 lbs?

Enter your answer as a number rounded to two decimal places.

0

Bonus:
Explain a process you could use to check #6 for reasonableness. You will use the internet.

The Brown's adopted a 6-week-old puppy that weighed 8 pounds.  The table below shows the weight of the puppy each week thereafter.  Find which model best fits the data, then find the age (in weeks) at which the puppy will weigh 50 lbs.

1

Which model best fits this data?

1

At what age (in weeks) will the puppy weight 50 pounds?

Hint: be careful what is input and what is output.

Enter your answer as an integer.

The notes of a musical scale and their frequencies are given in the table below.  Find the model that would best fit the data, and use the model to estimate the frequency of the note G (x= 7)

Hint:  If you get an error for a function, it is probably not the right one...

1

Which model best suits the data?

1

When using STAT to find regression curves, Dr. Demo got the following results.

Linear Regression: r = .99507
Quadratic Regression: r = .99932
Logarithmic Regression: = .99618
Exponential Regression: r = .99937

Which model best suits his data?

1

Review
Solve the equation.

(1.05)12x = 2.16

Enter your answer as a number rounded to three decimal places.

1

Review
Solve the equation.

73 - 20e1-2x = 60

Enter your answer as a number rounded to three decimal places.

1

What is the percentage growth/decay for the following function, per unit of x?

f(x) = 21 \cdot (2.51)^{.44x}

Enter your answer as a number rounded to three decimal places.

1

What is the percentage growth/decay for the following function, per unit of x?

f(x) = .996 \cdot (0.997)^{12x}

Enter your answer as a number rounded to three decimal places.

1

Rand earns 3% annual interest. What is his equivalent monthly interest, as a percent?

Enter your answer as a number rounded to 3 decimal places.

Review:
For the following questions, 
f(x) = 3(0.25)^{x+1}-2

1

Does the function represent exponential growth or decay?

1

Review:
For the following questions, 
f(x) = \frac{1}{2}(1.003)^{12x}

1

Does the function represent exponential growth or decay?

1

Review:
For the following questions, 
f(x) = 2\cdot ln(x+3)

1

What is the asymptote?

1

What is the x-intercept?

Use (x, y) format, with exactly one space after the comma.

1

What is the y-intercept?

Use (x, y) format, with exactly one space after the comma. Round to three decimal places

1

HW6: Mixed Models (2-day)

Categorize each situation by the type of function that would be the best model. You may use the internet as a resource

Categorize the situations according to the model best suited for them. Feel free to look up some equations.

Put the following functions in decreasing order based on their values as x \rightarrow \inftyHint: It may help to graph in Desmos and zoom out.

What is the value of growth/decay rate, as a percent? Enter your answer as an integer.

What is the value of the car in 2016, in dollars? Use four decimal places for the base.Enter your answer as a number rounded to two decimal places. For example, if your answer were $12.366, you would enter "12.37".

According to your model, what is the BMI of a female that weighs 130 lbs?Enter your answer as a number rounded to two decimal places.

Bonus:Explain a process you could use to check #6 for reasonableness. You will use the internet.

Which model best fits this data?

At what age (in weeks) will the puppy weight 50 pounds? Hint: be careful what is input and what is output.Enter your answer as an integer.

Which model best suits the data?

When using STAT to find regression curves, Dr. Demo got the following results.Linear Regression: r = .99507Quadratic Regression: r = .99932Logarithmic Regression: = .99618Exponential Regression: r = .99937Which model best suits his data?

ReviewSolve the equation.(1.05)12x = 2.16Enter your answer as a number rounded to three decimal places.

ReviewSolve the equation.73 - 20e1-2x = 60Enter your answer as a number rounded to three decimal places.

What is the percentage growth/decay for the following function, per unit of x?f(x) = 21 \cdot (2.51)^{.44x}Enter your answer as a number rounded to three decimal places.

What is the percentage growth/decay for the following function, per unit of x?f(x) = .996 \cdot (0.997)^{12x}Enter your answer as a number rounded to three decimal places.

Rand earns 3% annual interest. What is his equivalent monthly interest, as a percent?Enter your answer as a number rounded to 3 decimal places.

Does the function represent exponential growth or decay?

Does the function represent exponential growth or decay?

What is the asymptote?

What is the x-intercept?Use (x, y) format, with exactly one space after the comma.

What is the y-intercept?Use (x, y) format, with exactly one space after the comma. Round to three decimal places

Categorize each situation by the type of function that would be the best model. You may use the internet as a resource

Categorize the situations according to the model best suited for them. Feel free to look up some equations.

Put the following functions in decreasing order based on their values as x \rightarrow \inftyHint: It may help to graph in Desmos and zoom out.

What is the value of growth/decay rate, as a percent? Enter your answer as an integer.

What is the value of the car in 2016, in dollars? Use four decimal places for the base.Enter your answer as a number rounded to two decimal places. For example, if your answer were $12.366, you would enter "12.37".

According to your model, what is the BMI of a female that weighs 130 lbs?Enter your answer as a number rounded to two decimal places.

Bonus:Explain a process you could use to check #6 for reasonableness. You will use the internet.

Which model best fits this data?

At what age (in weeks) will the puppy weight 50 pounds? Hint: be careful what is input and what is output.Enter your answer as an integer.

Which model best suits the data?

What is the frequency of the note G (x=7)?Enter you answer as a number rounded to two decimal places.

When using STAT to find regression curves, Dr. Demo got the following results.Linear Regression: r = .99507Quadratic Regression: r = .99932Logarithmic Regression: = .99618Exponential Regression: r = .99937Which model best suits his data?

ReviewSolve the equation.(1.05)12x = 2.16Enter your answer as a number rounded to three decimal places.

ReviewSolve the equation.73 - 20e1-2x = 60Enter your answer as a number rounded to three decimal places.

What is the percentage growth/decay for the following function, per unit of x?f(x) = 21 \cdot (2.51)^{.44x}Enter your answer as a number rounded to three decimal places.

What is the percentage growth/decay for the following function, per unit of x?f(x) = .996 \cdot (0.997)^{12x}Enter your answer as a number rounded to three decimal places.

Rand earns 3% annual interest. What is his equivalent monthly interest, as a percent?Enter your answer as a number rounded to 3 decimal places.

Does the function represent exponential growth or decay?

What is the percent rate of growth/decay?Enter your answer as an integer.

What is the asymptote?

Select the end behaviors for f(x).Select two.

Does the function represent exponential growth or decay?

What is the asymptote?

What is the percent rate of growth/decay?Enter your answer as a number rounded to 1 decimal place.

Select the end behaviors for f(x).Select two.

What is the asymptote?

What is the x-intercept?Use (x, y) format, with exactly one space after the comma.

What is the y-intercept?Use (x, y) format, with exactly one space after the comma. Round to three decimal places

Select the end behaviors for f(x).Select two.

What is the frequency of the note G (x=7)?Enter you answer as a number rounded to two decimal places.

What is the percent rate of growth/decay?Enter your answer as an integer.

What is the asymptote?

Select the end behaviors for f(x).Select two.

What is the asymptote?

What is the percent rate of growth/decay?Enter your answer as a number rounded to 1 decimal place.

Select the end behaviors for f(x).Select two.

Select the end behaviors for f(x).Select two.

Put the following functions in decreasing order based on their values as x \rightarrow \infty

Hint: It may help to graph in Desmos and zoom out.

What is the value of growth/decay rate, as a percent?

Enter your answer as an integer.

What is the value of the car in 2016, in dollars?

Use four decimal places for the base.

Enter your answer as a number rounded to two decimal places. For example, if your answer were $12.366, you would enter "12.37".

According to your model, what is the BMI of a female that weighs 130 lbs?

Enter your answer as a number rounded to two decimal places.

Bonus:
Explain a process you could use to check #6 for reasonableness. You will use the internet.

At what age (in weeks) will the puppy weight 50 pounds?

Hint: be careful what is input and what is output.

Enter your answer as an integer.

When using STAT to find regression curves, Dr. Demo got the following results.

Linear Regression: r = .99507
Quadratic Regression: r = .99932
Logarithmic Regression: = .99618
Exponential Regression: r = .99937

Which model best suits his data?

Review
Solve the equation.

(1.05)12x = 2.16

Enter your answer as a number rounded to three decimal places.

Review
Solve the equation.

73 - 20e1-2x = 60

Enter your answer as a number rounded to three decimal places.

What is the percentage growth/decay for the following function, per unit of x?

f(x) = 21 \cdot (2.51)^{.44x}

Enter your answer as a number rounded to three decimal places.

What is the percentage growth/decay for the following function, per unit of x?

f(x) = .996 \cdot (0.997)^{12x}

Enter your answer as a number rounded to three decimal places.

Rand earns 3% annual interest. What is his equivalent monthly interest, as a percent?

Enter your answer as a number rounded to 3 decimal places.

What is the x-intercept?

Use (x, y) format, with exactly one space after the comma.

What is the y-intercept?

Use (x, y) format, with exactly one space after the comma. Round to three decimal places

Put the following functions in decreasing order based on their values as x \rightarrow \infty

Hint: It may help to graph in Desmos and zoom out.

What is the value of growth/decay rate, as a percent?

Enter your answer as an integer.

What is the value of the car in 2016, in dollars?

Use four decimal places for the base.

Enter your answer as a number rounded to two decimal places. For example, if your answer were $12.366, you would enter "12.37".

According to your model, what is the BMI of a female that weighs 130 lbs?

Enter your answer as a number rounded to two decimal places.

Bonus:
Explain a process you could use to check #6 for reasonableness. You will use the internet.

At what age (in weeks) will the puppy weight 50 pounds?

Hint: be careful what is input and what is output.

Enter your answer as an integer.

What is the frequency of the note G (x=7)?

Enter you answer as a number rounded to two decimal places.

When using STAT to find regression curves, Dr. Demo got the following results.

Linear Regression: r = .99507
Quadratic Regression: r = .99932
Logarithmic Regression: = .99618
Exponential Regression: r = .99937

Which model best suits his data?

Review
Solve the equation.

(1.05)12x = 2.16

Enter your answer as a number rounded to three decimal places.

Review
Solve the equation.

73 - 20e1-2x = 60

Enter your answer as a number rounded to three decimal places.

What is the percentage growth/decay for the following function, per unit of x?

f(x) = 21 \cdot (2.51)^{.44x}

Enter your answer as a number rounded to three decimal places.

What is the percentage growth/decay for the following function, per unit of x?

f(x) = .996 \cdot (0.997)^{12x}

Enter your answer as a number rounded to three decimal places.

Rand earns 3% annual interest. What is his equivalent monthly interest, as a percent?

Enter your answer as a number rounded to 3 decimal places.

What is the percent rate of growth/decay?

Enter your answer as an integer.

Select the end behaviors for f(x).

Select two.

What is the percent rate of growth/decay?

Enter your answer as a number rounded to 1 decimal place.

Select the end behaviors for f(x).

Select two.

What is the x-intercept?

Use (x, y) format, with exactly one space after the comma.

What is the y-intercept?

Use (x, y) format, with exactly one space after the comma. Round to three decimal places

Select the end behaviors for f(x).

Select two.

What is the frequency of the note G (x=7)?

Enter you answer as a number rounded to two decimal places.

What is the percent rate of growth/decay?

Enter your answer as an integer.

Select the end behaviors for f(x).

Select two.

What is the percent rate of growth/decay?

Enter your answer as a number rounded to 1 decimal place.

Select the end behaviors for f(x).

Select two.

Select the end behaviors for f(x).

Select two.