EXPONENTIAL FUNCTION AND LINEAR FUNCTIONS PRACTICE PROBLEMS

Problem 1 :

The number of dandelions in a large park is recorded over the course of five months, as shown in the table below.

which of the following best describes the relationship between time and the number of dandelions during the five months ?

a) Increasing linear           b) Decreasing linear

c) Exponential growth       d)  Exponential decay

Solution

Problem 2 :

The number of subscribers S, to a magazine increases by 21 percent each year. If the current number of subscribers to the magazine is 3000, which of the following equation models the number of subscribers to the magazine h half years from now ?

a) S = 3000(1.1)^h           b) S = 3000(1.21)^h

c) S = 3000(1.01)^h        d)  S = 3000(1.4641)^h 

Solution

Problem 3 :

The total amount of water w, in gallons left in a tank can be modeled by the equation w = 300 - 5t, where t is the number of hours since the tank started leaking. Which of the following is the best interpretation of the number 5 in the equation ?

a) The tank is empty after 5 hours.

b) The tank loses 5 gallons of water each hour.

c)  the tank continues to lost water until 5 gallons are left.

d)  Each hour, the tank loses 5 less gallons of water than it did the previous hour.

Solution

Problem 4 :

Tom buys a pack of baseball cards everyday. Each pack contains 7 cards but he gives away the two least valuable ones to his brother. Which of the following best describes the relationship between time (in days) and the total number of baseball cards in Tom's collection ?

a) Increasing linear           b) Decreasing linear

c) Exponential growth       d)  Exponential decay

Solution

Problem 5 :

Anna opens a bank account with an initial deposit of $1000. The bank account will earn 3 percent interest compounded annually for the first 5 years, after which it will earn 7 percent interest compounded annually. Which of the following expressions represents the total amount in the account after t years, where t > 5 ?

a)  1000 (1.03)⁵ (1.07)^t            b)  1000 (1.03)^t-5  (1.07)^t

c)  1000 (1.03)⁵ (1.07)^t-5            d)  1000 (1.03)⁵  (1.07)^t+5 

Solution

Problem 6 :

A house is losing a fourth of its value every year. Which of the following best describes the relationship between time (in years) and the value of house ?

a) Increasing linear           b) Decreasing linear

c) Exponential growth       d)  Exponential decay

Solution