Modeling Exponential Functions

An antibiotic is introduced into a colony of 12,000 bacteria during a laboratory experiment. The colony is decreasing by 15% per minute. Which function can be used to model the number of bacteria in the colony after x minutes?

• f(x) = 12000(1.15)^x

• f(x) = 12000(0.15)^x

• f(x) = 12000(0.85)^x

• f(x) = 12000(1.85)^x

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CCSS.HSF.LE.A.2

A vehicle worth $10,000 depreciates by 25% every 3 months. What will its value be after 2 years?

• V=10,000(0.75)^4, V=$3,164.06 = $3,164.06

• V=10,000(0.75)^6, V=$1,780.72 = $1,780.72

• V=10,000(0.75)^8, V=$1,001.93 = $1,001.93

• V=10,000(0.75)^7, V=$1,335.94 = $1,335.94

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CCSS.HSF.BF.A.2

A $2,000 machine loses 15% of its value every 6 months. What will its value be in 3 years?

• V=2,000(0.85)^4, V=$1,296.50 = $1,296.50

• V=2,000(0.85)^6, V=$748.57 = $748.57

• V=2,000(0.85)^3, V=$1,428.75 = $1,428.75

• V=2,000(0.85)^5, V=$936.79 = $936.79

A new camera costs $900 and loses 20% of its value every 3 months. How much will it be worth after 1 year?

A gaming console costs $500 and depreciates by 30% every 6 months. What will the value of the console be after 2 years?

• V=500(0.7)^3, V=$171.50

• V=500(0.7)^2, V=$245.00

• V=500(0.7)^4, V=$120.05

• V=500(0.7)^5, V=$84.03

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CCSS.HSF.BF.A.2

A $5,000 computer depreciates by 35% every 6 months. What will be its value after 2 years?

• V=5,000(0.65)^3, V=$1,096.25 = $1,096.25

• V=5,000(0.65)^4, V=$750.00 = $750.00

• V=5,000(0.65)^5, V=$487.50 = $487.50

A smartphone worth $800 loses 10% of its value every 3 months. How much will it be worth after 2 years?

A $7,500 printer depreciates by 5% every 3 months. What is its value after 5 years?

A $3,000 treadmill depreciates by 12% every 6 months. What will its value be in 3 years?

Sophia invested $1,000 in equipment that depreciates by 40% every 6 months. What is the value of the equipment after 1.5 years?