Understanding and Graphing Logarithmic Functions

A scientist is studying the growth of bacteria. The number of bacteria doubles every hour. If the initial count is 100, how many hours will it take for the bacteria to reach 800? Graph the function and identify its type.

• 4 hours

• 2 hours

• 3 hours

• 5 hours

A city’s population is modeled by the equation P(t) = 5000 * log(t + 1), where P is the population and t is the number of years since 2000. How many years will it take for the population to reach 10,000? Graph the function and identify its characteristics.

• 150 years

• 200 years

• 99 years

• 50 years

A phone company finds that the number of users can be modeled by the equation U(t) = 200 * log(t + 1), where U is the number of users in thousands and t is the time in years. How many users will there be after 3 years? Graph the function and identify its type.

• 120420

• 130000

• 100000

• 150000

A tree grows in height according to the equation H(t) = 2 * log(t + 1), where H is the height in meters and t is the age of the tree in years. How tall will the tree be when it is 5 years old? Graph the function and describe its behavior.

• 4.10 meters

• 0.75 meters

• 3.25 meters

• 1.56 meters

A bank account earns interest according to the formula A(t) = 1000 * log(1 + rt), where A is the amount in dollars, r is the interest rate, and t is time in years. If r = 0.05, how much will be in the account after 10 years? Graph the function and identify its type.

• 150.5

• 250.3

• 200.0

• 176.1

A student is studying the relationship between the number of hours studied and test scores. The score can be modeled by S(h) = 50 + 10 * log(h + 1). If a student studies for 4 hours, what will their score be? Graph the function and identify its type.

• 70

• 60

• 57

• 45

A population of fish in a lake is modeled by the equation F(t) = 300 * log(t + 1), where F is the fish population and t is the time in years. How many fish will there be after 2 years? Graph the function and describe its behavior.

• 400

• 500

• 250

• 330

A company’s profit can be modeled by the equation P(x) = 500 * log(x + 1), where P is the profit in dollars and x is the number of products sold. If the company sells 10 products, what will be the profit? Graph the function and identify its type.

• 600 dollars

• 520.7 dollars

• 300 dollars

• 450.5 dollars