Application of Exponential Function

An equation in the form y=b^x will represent decay if...

• b < 0

• b > 1

• 0 < b < 1

Which of the following functions represents exponential DECAY? (Select ALL that apply)

• f(x) = 7⋅(2/3)^x

• f(x) = 7⋅(3/2)^x

• f(x)= (1/2)⋅(3)^x

• f(x)= (2)⋅(.33)^x

Gasoline costs $1.99 per gallon. If the price per gallon increases an average of 6% per month, which function models the exponential growth of the pricing?

• 1.06(1.99)^t

• 1.99(1.06)^t

• [1.06(1.99)]^t

• 1.99(.94)^t

You put $2000 in the bank and earn interest at a 2.5% rate compounded monthly. How much will you have after 15 years?

• $30,758.65

• $2,001.56

• $2,908.85

• $2,896.60

Most automobiles depreciate as they get older. Suppose an automobile that originally costs $14,000 depreciates by 20% of its value every year. 
What exponential equation can we create to model this situation?

• y=14000(.20)^x
• y=14000(.80)^x
• y=14000(1+.20)^x
• y=14000(1+.80)^x

A sculpture is increasing in value at a rate of 9% per year, and its value in 2000 was $1500. Write an exponential growth function to model this situation.

• f(t)=1500(1.09)^t
• f(t)=1500(0.09)^t
• f(t)=2000(0.09)^t
• f(t)=1500(9)^t

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x
• y=30(5000)^x
• y=5000(1.3)^x
• y=5000x^x

Which of the following is an increasing exponential function whose y-intercept is 50?

• y = 50(.05)^x
• y = 50x - 4
• y = (2)^x + 50
• y = 50(1.4)^x

Identify the percent (%) increase or decrease for the following function.

f(x) = 35 (1 – 0.06)^x

• Increase by 6%

• Decrease by 0.06%

• Increase by 0.06%

• Decrease by 6%

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

• $23,219.72
• $136.72
• $51,710.94
• $16,710.94