Quiz 7.2 - Properties, Applications, and Mixed Modelling

Last updated about 4 years ago

16 questions

5

1

2

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Quiz 7.2 - Properties, Applications, and Mixed Modelling

Last updated about 4 years ago

16 questions

5

Draggable item		Corresponding Item

1

Given the exponential function y=104(.77)^{x}, what is the percentage rate of growth/decay?

Enter your answer as an integer, no "%" or spaces.

1

Given the following exponential function determine the percentage rate of increase or decrease per unit of x.

y=(4)^{-2x}

Enter your answer as a 4-digit number.

1

2

A biologist is studying the growth of a bacterial colony in a petri dish.  The table below shows the number of cells in the petri dish after some weeks during the study.



When finding a regression model, the biologist gets the following values for r:
Linear: 0.8233
Quadr: 0.9804
Expon: 0.9905
Logar:  0.6934

1

The table below lists the time it takes for a turkey to reach certain temperatures after being pulled from a hot oven.

When finding a regression model, a student gets the following values for r:

Linear: 0.9068
Expon: error 
Logar:  0.9708

1

Match the expressions using the properties of logarithms or exponents.

(Hint: You can try these out in your calculator by setting a, m, and n to different numbers.)

Draggable item		Corresponding Item
log_{b} (x)		a^{m+n}
a^{m}\cdot a^{n}		(ab)^{m}
\frac{a^{m}}{a^{n}}		a^{m\cdot n}
a^{m}\cdot b^{m}		\sqrt[n]{a}
a^{\frac{1}{n}}		a^{m-n}
(a^{m})^{n}		\frac{ln(x)}{ln(b)}

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease.

y=420(.981)^{x}

growth at 98.1%

decay at 98.1%

decay at 1.9%

growth at 1.9%

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease.

y=800(1.078)^{x}

growth at 1.078%

decay at 1.078%

decay at 7.8%

growth at 7.8%

Given the exponential function y=104(.77)^{x}, what is the percentage rate of growth/decay?

Enter your answer as an integer, no "%" or spaces.

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease per unit of x.

y=800(2.718)^{0.244x}

growth at 24.4%

growth at 27.6%

decay at 24.4%

decay at 27.6%

Given the following exponential function determine the percentage rate of increase or decrease per unit of x.

y=(4)^{-2x}

Enter your answer as a 4-digit number.

growth at 2.5% every minute

growth at 2.5% every 7500 minutes

decay at 2.5% every minute

decay at 2.5% every 7500 minutes

The function f(t) = 9200(0.79)^{t} represents the change in a quantity over t years. What does the constant 0.79 reveal about the rate of change of the quantity?

(Hint: find the equivalent monthly rate.)

f(t)=780(1.0297)^{12t}

f(t)=780(1.42)^{12t}

f(t)=780(1.0297)^{t}

f(t)=780(1.42)^{\frac{1}{12}t}

Dan and Ben invested the same amount in savings. Dan earns a certain rate of monthly interest, while Ben earns a certain rate of yearly interest. If they both end the year with the same amount of interest collected, who's interest rate is greater, Dan's or Ben's?

There is not enough information to determine this.

Ben's interest rate is greater than Dan's.

They have the same interest rate.

Dan's interest rate is greater than Ben's.

Categorize the following situations by the model that best suits them.

The amount of gas in a tank after some distance driving.
The value of a savings account some time after collecting interest.
The path of a rock some time after it is launched from a catapult.
The population of rabbits after some time without predation.
The total amount of calories consumed after eating some number of M&Ms.

Linear
Quadratic
Exponential Growth

A biologist is studying the growth of a bacterial colony in a petri dish.  The table below shows the number of cells in the petri dish after some weeks during the study.



When finding a regression model, the biologist gets the following values for r:
Linear: 0.8233
Quadr: 0.9804
Expon: 0.9905
Logar:  0.6934

1

What will be the number of cells in week 6?

Round to the nearest whole number.

1

In what week will the number of cells reach one billion (1,000,000,000)?

Enter your answer as a number rounded to the nearest tenth.

The table below lists the time it takes for a turkey to reach certain temperatures after being pulled from a hot oven.

When finding a regression model, a student gets the following values for r:

Linear: 0.9068
Expon: error 
Logar:  0.9708

1

Estimate the number of minutes the turkey will take to cool to a temperature of 70.

Enter your answer as a number rounded to the nearest tenth.

Note: it will be in between two of the time values, which is strange. It's okay.

Match the expressions using the properties of logarithms or exponents.

(Hint:  You can try these out in your calculator by setting a, m, and n to different numbers.)

log_{b} (x)

a^{m+n}

a^{m}\cdot a^{n}

(ab)^{m}

\frac{a^{m}}{a^{n}}

a^{m\cdot n}

a^{m}\cdot b^{m}

\sqrt[n]{a}

a^{\frac{1}{n}}

a^{m-n}

(a^{m})^{n}

\frac{ln(x)}{ln(b)}

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease.

y=420(.981)^{x}

growth at 98.1%

decay at 98.1%

decay at 1.9%

growth at 1.9%

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease.

y=800(1.078)^{x}

growth at 1.078%

decay at 1.078%

decay at 7.8%

growth at 7.8%

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease per unit of x.

y=800(2.718)^{0.244x}

growth at 24.4%

growth at 27.6%

decay at 24.4%

decay at 27.6%

growth at 2.5% every minute

growth at 2.5% every 7500 minutes

decay at 2.5% every minute

decay at 2.5% every 7500 minutes

The function f(t) = 9200(0.79)^{t} represents the change in a quantity over t years.  What does the constant 0.79 reveal about the rate of change of the quantity?

growth at 79% every day

growth at 79% every year

decay at 21% every day

growth at 21% every day

decay at 21% every year

decay at 79% every year

(Hint:  find the equivalent monthly rate.)

f(t)=780(1.0297)^{12t}

f(t)=780(1.42)^{12t}

f(t)=780(1.0297)^{t}

f(t)=780(1.42)^{\frac{1}{12}t}

Dan and Ben invested the same amount in savings.  Dan earns a certain rate of monthly interest, while Ben earns a certain rate of yearly  interest.  If they both end the year with the same amount of interest collected, who's interest rate is greater, Dan's or Ben's?

There is not enough information to determine this.

Ben's interest rate is greater than Dan's.

They have the same interest rate.

Dan's interest rate is greater than Ben's.

Categorize the following situations by the model that best suits them.

The amount of gas in a tank after some distance driving.

The value of a savings account some time after collecting interest.

The path of a rock some time after it is launched from a catapult.

The population of rabbits after some time without predation.

The total amount of calories consumed after eating some number of M&Ms.

Linear

Quadratic

Exponential Growth

Based on the r-values, what model best fits this data?

Linear

Quadratic

Exponential

Logarithmic

What will be the number of cells in week 6?

Round to the nearest whole number.

In what week will the number of cells reach one billion (1,000,000,000)?

Enter your answer as a number rounded to the nearest tenth.

According the r-values given, which model best suits the data?

Linear

Exponential

Logarithmic

Estimate the number of minutes the turkey will take to cool to a temperature of 70.

Enter your answer as a number rounded to the nearest tenth.

Note: it will be in between two of the time values, which is strange. It's okay.

Based on the r-values, what model best fits this data?

Linear

Quadratic

Exponential

Logarithmic

According the r-values given, which model best suits the data?

Linear

Exponential

Logarithmic

Quiz 7.2 - Properties, Applications, and Mixed Modelling

Quiz 7.2 - Properties, Applications, and Mixed Modelling

Given the exponential function y=104(.77)^{x}, what is the percentage rate of growth/decay?Enter your answer as an integer, no "%" or spaces.

Given the following exponential function determine the percentage rate of increase or decrease per unit of x.y=(4)^{-2x}Enter your answer as a 4-digit number.

Match the expressions using the properties of logarithms or exponents.(Hint: You can try these out in your calculator by setting a, m, and n to different numbers.)

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease.y=420(.981)^{x}

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease.y=800(1.078)^{x}

Given the exponential function y=104(.77)^{x}, what is the percentage rate of growth/decay?Enter your answer as an integer, no "%" or spaces.

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease per unit of x.y=800(2.718)^{0.244x}

Given the following exponential function determine the percentage rate of increase or decrease per unit of x.y=(4)^{-2x}Enter your answer as a 4-digit number.

The function f(t) = 9200(0.79)^{t} represents the change in a quantity over t years. What does the constant 0.79 reveal about the rate of change of the quantity?

(Hint: find the equivalent monthly rate.)

Dan and Ben invested the same amount in savings. Dan earns a certain rate of monthly interest, while Ben earns a certain rate of yearly interest. If they both end the year with the same amount of interest collected, who's interest rate is greater, Dan's or Ben's?

Categorize the following situations by the model that best suits them.

What will be the number of cells in week 6?Round to the nearest whole number.

In what week will the number of cells reach one billion (1,000,000,000)?Enter your answer as a number rounded to the nearest tenth.

Estimate the number of minutes the turkey will take to cool to a temperature of 70.Enter your answer as a number rounded to the nearest tenth.Note: it will be in between two of the time values, which is strange. It's okay.

Based on the r-values, what model best fits this data?

What will be the number of cells in week 6?Round to the nearest whole number.

In what week will the number of cells reach one billion (1,000,000,000)?Enter your answer as a number rounded to the nearest tenth.

According the r-values given, which model best suits the data?

Estimate the number of minutes the turkey will take to cool to a temperature of 70.Enter your answer as a number rounded to the nearest tenth.Note: it will be in between two of the time values, which is strange. It's okay.

Given the exponential function y=104(.77)^{x}, what is the percentage rate of growth/decay?

Enter your answer as an integer, no "%" or spaces.

Given the following exponential function determine the percentage rate of increase or decrease per unit of x.

y=(4)^{-2x}

Enter your answer as a 4-digit number.

Match the expressions using the properties of logarithms or exponents.

(Hint: You can try these out in your calculator by setting a, m, and n to different numbers.)

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease.

y=420(.981)^{x}

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease.

y=800(1.078)^{x}

Given the exponential function y=104(.77)^{x}, what is the percentage rate of growth/decay?

Enter your answer as an integer, no "%" or spaces.

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease per unit of x.

y=800(2.718)^{0.244x}

Given the following exponential function determine the percentage rate of increase or decrease per unit of x.

y=(4)^{-2x}

Enter your answer as a 4-digit number.

What will be the number of cells in week 6?

Round to the nearest whole number.

In what week will the number of cells reach one billion (1,000,000,000)?

Enter your answer as a number rounded to the nearest tenth.

Estimate the number of minutes the turkey will take to cool to a temperature of 70.

Enter your answer as a number rounded to the nearest tenth.

Note: it will be in between two of the time values, which is strange. It's okay.

What will be the number of cells in week 6?

Round to the nearest whole number.

In what week will the number of cells reach one billion (1,000,000,000)?

Enter your answer as a number rounded to the nearest tenth.

Estimate the number of minutes the turkey will take to cool to a temperature of 70.

Enter your answer as a number rounded to the nearest tenth.

Note: it will be in between two of the time values, which is strange. It's okay.