MTHS 105 - Applied College Algebra Exam 1 Answers

Question 1

The following table gives the values $D=f(t)$, the total US debt (in $ billions) $t$ years after 2005

T-Years

Billions of

Dollars

7932.7

8507.0

9007.7

10,024.7

11,909.8

13,561.6

14,790.3

16,066.2

16,738.2

What does the following statement represent? \[ \frac{f(5)-f(3)}{5-3}\]

Answer: The average rate of change between 2008 and 2010 is $1768.45 billions of dollars . Or, you could say the total US debt is at a rate of $1768.45 billion dollars per year between 2008 and 2010.

What does the following statement represent? \[ \frac{f(8)-f(5)}{8-5}\]

Answer: The average rate of change between 2010 and 2013 is $1058.87 billions of dollars . Or, you could say the total US debt is at a rate of $1058.87 billion dollars per year between 2010 and 2013.

Question 2

Atmospheric levels of Carbon Dioxide have risen from 336 parts per million (ppm) in 1979 to 396 ppm in 2014. Find the average rate of change of CO$_2$ levels during this time period.

The average rate of change between 1979 to 2014 is 1.71ppm per year.

Atmospheric levels of Carbon Dioxide have risen from 336 parts per million (ppm) in 1979 to 396 ppm in 2016. Find the average rate of change of CO$_2$ levels during this time period.

The average rate of change between 1979 to 2016 is 1.62ppm per year.

Question 3

A homing pigeon starts 1000 miles from home and flies 5 miles toward home each day. Express the distance from home in miles, D as a function of the number of days, d.

\[D=1000-5d\]

A homing pigeon starts 1000 miles from home and flies 15 miles toward home each day. Express the distance from home in miles, D as a function of the number of days, d.

\[D=1000-15d\]

Question 4

The population of a town is given by $P=350t+5000$ where $t$ is the years after 1980

Independent Variable is T, Dependent is P
After 10 years, the population will be 8500 people. In 1990, the population will be 8500 people

The population of a town is given by $P=350t+5000$ where $t$ is the years after 1983

Independent Variable is T, Dependent is P
After 10 years, the population will be 8500 people. In 1993, the population will be 8500 people

Question 5

Last month, Costco sold 55 new memberships. The Gold memberships sold for $10.50 each and the Business memberships sold for $15.50 each. If the total sales for the new memberships were $682.50 last month, how many of each membership were sold?

21 Business Memberships and 34 Gold Memberships

Find a possible formula for a linear function if $f(-30)=20$ and $f(20)= -50$.

$y=-\frac{7}{5}x-22$

Question 6

The required cooling capacity, in BTUs for a room air conditioner is proportional to the area of the room being cooled. A room that is 280 square feet requires an air conditioner whose cooling capacity is 7000 BTUs. (Note, we are neglecting volume)

$k = 25$

The required cooling capacity, in BTUs for a room air conditioner is directly proportional to the area of the room being cooled. A room that is 280 square feet requires an air conditioner whose cooling capacity is 8000 BTUs. (Note, we are neglecting volume)

$k=28.57$

Question 7

Solve the following formula for $q_2$

\[F=\frac{Gq_1q_2}{r^2}\]

Answer:

$$q_2 = \frac{Fr^2}{Gq_1}$$

Find the mistake? Yes, there is a mistake somewhere.

Question 8

At the gas station, the revenue $R$ varies directly with the amount of gasoline sold, in gallons. If the revenue is $47.40 when 12 gallons of gas are sold, what’s the revenue when 20.25 gallons of gas are sold.

$79.98

Clint is buying large bottles of lemonade and small bottles of soda for a party.Each bottle of lemonade costs $6 and each bottle of soda costs $2. He wants to spend exactly $40 on drinks. Write an equation to represent the situation.

$6L+2S=40$

Question 9

Find the mistake? Yes, there is a mistake somewhere.

At the gas station, the revenue $R$ varies directly with the amount of gasoline sold, in gallons. If the revenue is $47.40 when 12 gallons of gas are sold, what’s the revenue when 18.25 gallons of gas are sold.

$72.09

Question 10

Write an equation that has a slope of 5 and it passes through the point $(-1,-8)$

$y=5x-3$

Solve the following equation

\[5y+7+3y=5(2y+1)-8\]

$y=5$

MTHS 105 - Applied College Algebra Exam 1 Answers

James Boffenmyer

09/22/25

Question 1

The following table gives the values \(D=f(t)\), the total US debt (in $ billions) \(t\) years after 2005

What does the following statement represent? \[ \frac{f(5)-f(3)}{5-3}\]

What does the following statement represent? \[ \frac{f(8)-f(5)}{8-5}\]

Question 2

Atmospheric levels of Carbon Dioxide have risen from 336 parts per million (ppm) in 1979 to 396 ppm in 2014. Find the average rate of change of CO\(_2\) levels during this time period.

Atmospheric levels of Carbon Dioxide have risen from 336 parts per million (ppm) in 1979 to 396 ppm in 2016. Find the average rate of change of CO\(_2\) levels during this time period.

Question 3

A homing pigeon starts 1000 miles from home and flies 5 miles toward home each day. Express the distance from home in miles, D as a function of the number of days, d.

\[D=1000-5d\]

A homing pigeon starts 1000 miles from home and flies 15 miles toward home each day. Express the distance from home in miles, D as a function of the number of days, d.

\[D=1000-15d\]

Question 4

The population of a town is given by \(P=350t+5000\) where \(t\) is the years after 1980

The population of a town is given by \(P=350t+5000\) where \(t\) is the years after 1983

Question 5

Last month, Costco sold 55 new memberships. The Gold memberships sold for $10.50 each and the Business memberships sold for $15.50 each. If the total sales for the new memberships were $682.50 last month, how many of each membership were sold?

Find a possible formula for a linear function if \(f(-30)=20\) and \(f(20)= -50\).

Question 6

The required cooling capacity, in BTUs for a room air conditioner is proportional to the area of the room being cooled. A room that is 280 square feet requires an air conditioner whose cooling capacity is 7000 BTUs. (Note, we are neglecting volume)

The required cooling capacity, in BTUs for a room air conditioner is directly proportional to the area of the room being cooled. A room that is 280 square feet requires an air conditioner whose cooling capacity is 8000 BTUs. (Note, we are neglecting volume)

Question 7

Solve the following formula for \(q_2\)

Find the mistake? Yes, there is a mistake somewhere.

Question 8

At the gas station, the revenue \(R\) varies directly with the amount of gasoline sold, in gallons. If the revenue is $47.40 when 12 gallons of gas are sold, what’s the revenue when 20.25 gallons of gas are sold.

Clint is buying large bottles of lemonade and small bottles of soda for a party.Each bottle of lemonade costs $6 and each bottle of soda costs $2. He wants to spend exactly $40 on drinks. Write an equation to represent the situation.

Question 9

Find the mistake? Yes, there is a mistake somewhere.

At the gas station, the revenue \(R\) varies directly with the amount of gasoline sold, in gallons. If the revenue is $47.40 when 12 gallons of gas are sold, what’s the revenue when 18.25 gallons of gas are sold.

Question 10

Write an equation that has a slope of 5 and it passes through the point \((-1,-8)\)

Solve the following equation