Modeling Decreasing Exponential Functions

A car was purchased for $25,000. Research shows that the car has an average yearly depreciation rate of 18.5%. Create a function that will determine the value, V(t), of the car t years after purchase.

• V(t) = 25000(1 - 0.185)^t

• V(t) = 25000(1 + 0.185)^t

• V(t) = 25000(1 - 18.5)^t

• V(t) = 25000(1 + 18.5)^t

The rabbit population started at 65,000 rabbits. The population is decreasing at a rate of 1.5% each year. Write a function r(t) to represent the rabbit population after t years.

• r(t) = 65000(1 - 0.015)^t

• r(t) = 65000(1 + 0.015)^t

• r(t) = 65000(1 - 1.5)^t

• r(t) = 65000(1 + 1.5)^t

The bear population in a given area is currently 1580. They anticipate the bear population to decrease by 2% each year. Which function represents the population of bears, B, after t years.

• B = 1580(0.02)

• B = 1580(1 – 0.02)

• B = 1580(1 + 0.02)

• B = 1580(1 – 0.2)

is it a growth factor or a decay factor?

• Growth Factor

• Decay Factor

Suppose a culture of bacteria begins with 500 cells and dies by 30% each year. Write an equation that represents this situation.

• y = 500(0.7)ⁿ

• y = 500(1.3)ⁿ

• y = 500(1.7)ⁿ

• y = 500(1.13)ⁿ

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

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=5000(1.3)^x

• y=30(5000)^x

• y=5000x^x

You bought a car for $25000 in 2010 that depreciates in value by 2% every year (not compounded continuously). State the equation A(t) that represents the value of the card after t  years.

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(0.92)^x

• y=15,000(1.08)^x

• y=15,000(0.08)^x

A computer worth $800 is expected to lose 28% of its value every year. Write a function that represents the value of the computer over time, t.

Please include "y=" in your answer. Don't forget the variable t.

Mathematical Equivalence

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