Unit 9 Review

For the functions f(x) = x⁶ and g(x) = 5^x which graph will increase faster as you move to the right?

• f(x), because 6 > 5

• f(x), because the base is increasing

• g(x), because the exponent is increasing

• They both will be equal because they both go to infinity

For the exponential function f(x) = 4^x - 3 what is the equation for the horizontal asymptote?

• y = -3

• x = -3

• y = 4

• There is no horizontal asymptote

Which of the following represents the domain and range for the exponential equation f(x) = (1/2)^x?

• Domain: All Real Numbers; Range: y ≥ 0

• Domain: All Real Numbers; Range: y > 0

• Domain: x ≥ 0; Range: All Real Numbers

• Domain: x > 0; Range: All Real Numbers

Which transformation of the graph of f(x) = 4^x will result in the graph of g(x) = 4^x - 3

• Shift f(x) up 3 units

• Shift f(x) left 3 units

• Shift f(x) right 3 units

• Shift f(x) down 3 units

The graph of f(x) = 15^x is shifted 3 units to the left to obtain the graph of g(x). What would be the equation of g(x)?

• g(x) = 15^{x - 3}

• g(x) = 15^{x + 3}

• g(x) = 15^x - 3

• g(x) = 15^x + 3

Which of these shows an exponential function with a base of 5? (Hint: Look at coordinate points)

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There are currently 800 bacteria in a petri dish. If the population of the bacteria in the dish triples every 4 hours, write the expression, f(n), that represents the number of bacteria n hours from now?

• f(n) = 800 x 3n

• f(n) = 800 x 3(n/4)

• f(n) = 800 x 3ⁿ

• f(n) = 800 x 3^(n/4)

A company commits to reducing its petroleum fuel use by 20% each year from the preceding year. If the company used 18,000 gallons of fuel in the year prior to starting the program, write a formula, f(n), that represents the fuel used during year n of the program?

• f(n) = 18,000^0.8n

• f(n) = 18,000(0.8)ⁿ

• f(n) = 18,000 - 0.8ⁿ

• f(n) = (18,000 ⋅ 0.8)ⁿ

Mrs. Anderson is saving to buy a car that costs $15,000. She has already saved $4,000 and decides to put all of this money into a new savings account. The money in this account will earn 5% interest, which is compounded monthly. Write the model that would be appropriate to determine how many years, y, Mrs. Anderson will have to wait until she has earned enough money in this account to buy the car?

• 15,000 = 4,000(1.05/12)^12y

• 4,000 = 15,000(1.05/12)^y

• 15,000 = 4,000(1 + 0.05/12)^12y

• 4,000 = 15,000(1 + 0.05/12)^12y

Ten grams of radium will decay according to the formula below, where A represents the number of grams remaining after t years.

R(t) = 10(½)^t/700

Approximately how many grams of radium will remain after 10 grams have decayed for 1600 years?

• 2.05 grams

• 1.8 grams

• 11.43 grams

• 8.5 grams