Exponential Functions Eoc Review

Jason compared the function f(x) = 20(1.2) ^x to the function that fits the values in the table g(x) above. 
What is the distance between the y-intercepts of the two functions?

• 14
• 8
• 6
• 4

What is the smallest positive integer value of x such that the value of f(x) = 2^x + 2 exceeds the value of g(x) =12x + 8?

• 4
• 5
• 6
• 7

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

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.

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 percent rate of decrease in population?

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

The number of employees in a company can be modeled by the equation P = 35(1.05)^x, where P is the total number of employees, and x represents the time, in years. Which statement is true?

• The number of employees increases by 5% each year.
• The number of employees decreases by 5% each year.
• The number of employees increases by 105% each year.
• The number of employees decreases by 105% each year.

A liquid is evaporating. The amount of a liquid remaining, in liters, after x weeks is modeled by the equation y = 100(0.78)^x.  Approximately what percent of the liquid evaporates per week?

• 22%
• 47%
• 53%
• 78%

• Function
• Not a Function