Exponential Growth and Decay Applications - Week 2 of RLD

Some banks charge a fee for a savings account that is left inactive for an extended period of time. The equation y = 5000(0.98)^x represents the amount remaining, y, of one account that was left inactive for a period of x years. What does the number 5000 represent in this situation?

• A fee charged for an inactive account

• The percent of money in the account after x years

• The amount of money in the account initially

• The amount of money in the account after x years

The function to find the value of a car after t years is given by v(t) = 24,000(.75)^tWhich of the following statements is not true?

• The starting value of the car was $24,000.

• The y-values of the graph increase as the x-values increase.

• The value 0.75 indicates this is an exponential decay situation.

• The horizontal asymptote is y = 0, which means the car will never have a value of $0.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x

• y = 15(1.35)^x

• y = 15(0.35)^x

• y = 35(1.15)^x

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?

• ^.08

• ^1.08

• .92

• 8

The value of your new laptop can be modeled by the equation  $y=2000\left(0.84\right)^t$  where t is the number of years you've had the laptop.  What is the annual depreciation rate of the laptop?

• 84%

• 0.84%

• 16%

• 0.16%

Your shiny new boat cost $7650. The depreciation for your boat is 14% per year. Which expression would allow you to estimate the value of your vehicle in 3 years?

• 7650(0.14)³

• 7650(.86)³

• 7650(1.86)³

• 7650(1.14)³

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 per month?

• y = 1.06(1.99)^t

• y = 1.99(1.06)^t

• y = [1.06(1.99)]^t

• y = 1.99(.94)^t

An antibiotic is introduced into a colony of 12,000 bacteria during a laboratory experiment. The colony is decreasing by 14.9% per minute. Which function can be used to model the number of bacteria in the colony after x minutes?

• f(x) = 12000(1 + 14.9)^x

• f(x) = 12000(1 - 14.9)^x

• f(x) = 12000(1 + 0.149)^x

• f(x) = 12000(1 - 0.149)^x

There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month. At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?

• f(x) = 417(3.75)^x

• f(x) = 417(0.0375)^x

• f(x) = 417(1.0375)^x

• f(x) = 417(1.375)^x

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

• y=8(15,000)^x

• y=15,000(1.08)^x

• y=15,000(0.92)^x

• y=15,000(0.08)^x