Math 1 EOC Bootcamp - Interpreting Meaning from Context

The value of property in a particular area depends on the land and the square footage of the house according to the equation given below, where x represents the square footage of the house, in square feet.
V=80x+6000
What is the meaning of the V-intercept and slope in this context?

• The V-intercept is the value of the house not including the land, and the slope is the rate of increase of the value of the house for each increase in square footage.
• The V-intercept is the value of the house not including the land, and the slope is the total value of the house and land.
• The V-intercept is the total value of the house and land, and the slope is the value of the house not including the land.
• The V-intercept is the rate of increase of the value of the house for each increase in square footage, and the slope is the value of the land without the house.

Which situation can be modeled using an exponential function?

• A tree grows 15 centimeters per year.
• A bacterial population decreases by 100 bacteria every hour.
• The money in a bank account grows by 1% per year.
• The rate a taxi driver charges is a fixed fee plus $0.30 per mile.

A population can be modeled by the function below, where t is time in years.
P(t) = 1200(1-0.05)^t
What is the meaning of 0.05 in this context?

• It is the rate of decrease of the population each year.
• It is the rate of increase of the population each year.
• It is the fraction of time needed for the population to decrease by 1.
• It is the fraction of time needed for the population to increase by 1.

A bacterial population, P, grows by 36% every hour for h hours. The initial population is 150. Which equation represents this bacterial population after h hours?

• P=150(0.36)^h
• P=150(1.36)^h
• P=150+(0.36)^h
• P=150+(1.36)^h

Jada is traveling to her college, which is 75 miles from her home, at a speed of 30 miles per hour. Which equation best represents the distance remaining to the college after x hours, and why?

• f(x)=75(0.70)^x; the function is exponential because the distance to the college decreases by a constant percentage each hour
• f(x)=75(1.30)^x; the function is exponential because the distance to the college increases by a constant percentage each hour
• f(x)=75-30x; the function is linear because the distance to the college decreases by a constant rate each hour
• f(x)=75+30x; the function is linear because the distance to the college increases by a constant rate each hour

Jerami is going to deposit an equal amount of money into a checking account each month until he has saved $2,000. The amount of money, y, in the account after x months can be modeled by the equation y=35x+250. What does the slope of the graph of the equation represent?

• The amount of money deposited monthly.
• The amount of money originally in the account.
• The number of months it would take to earn $250.
• The number of months it would take to reach $2,000.

Justin is comparing bank loans in order to buy a car. The summaries of the bank loans are shown below.
Bank 1 - a loan of $12,000 at a rate of 4.5% compounded monthly
Bank 2 - a loan of $15,000 with a payment of $500 a month
Which statement best describes the loans Justin is being offered by the two banks?

• Both loans represent linear functions.
• Both loans represent exponential functions.
• The loan from Bank 1 is linear, while the loan from Bank 2 is exponential.
• The loan from Bank 2 is linear, while the loan from Bank 1 is exponential.

Dan's football team brings a 5-gallon cooler of Powerade to every game so players can stay hydrated. The amount of Powerade in the cooler can be modeled by the equation y=5-0.2x, where y is the amount of Powerade in the cooler in gallons, and x is the number of players who have taken a drink of Powerade. Which best describes the amount, in gallons, of Powerade that is in the cooler at any time, x?

• The amount of Powerade in the cooler decreases at a constant rate.
• The amount of Powerade in the cooler increases at a constant rate.
• The amount of Powerade in the cooler decreases at an exponential rate.
• The amount of Powerade in the cooler increases at an exponential rate.

A population of bacteria in a lab is modeled by the function shown below, where t is the time in months.
P(t) = 100(0.94)^t
Based on the function, what is the rate of decrease in population?

• 6% each month
• 6% each year
• 94% each year
• 94% each month

The number of cell phone users for a particular plan, n, can be modeled by the function, n(t)=140(1+0.08)^t, where t is the time in months. According to the model, the number of cell phone users is growing at what rate per month?

• 1.08%
• 8%
• 140%
• 80%