Exponential Growth/Decay Word Problems

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

• f(x)=400(1+3)^x
• f(x)=400(1-0.03)^x
• f(x)=400(1+0.03)^x
• f(x)=400(0.03)^x

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CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

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

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CCSS.HSF.LE.A.2

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

Tags

CCSS.HSF.LE.A.2

A 78 gram sample of Uranium loses half of its mass each year.  What is the exponential equation? 

• y=78(0.5)^x
• y=78(1.5)^x
• y=78(2)^x

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CCSS.HSA.CED.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x
• y=6(1+14)^x
• y=6(1.14)^x
• y=6(0.86)^x

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CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

Your shiny new boat cost $7650.  The depreciation for your boat is 14% per year.  What is the equation that models this problem for the value of the vehicle in 3 years?

• y= 7650(.14)³
• y= 7650(.86)³
• y= 7650(1+.86/1)^3*1
• y= 7650(1.14)³

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CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Since January 1980, the population of the city of Brownville has grown according to the mathematical model y=720,500(1.022)^x, where x is the number of years since January 1980. What is the percentage increase of the population annually?

• 720,500%
• 102.2%
• 2.2%
• 22%

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CCSS.HSF-LE.A.1C

The number of farms in Indiana (in thousands) can be modeled by F = 115,000(.987)^t, where t is the number of years since 1980.  According to the equation, when will the number of farms in Indiana be about 50,000?

• 54 years
• 64 years
• 76 years
• 67 years

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CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

 Halle deposited $4000 into an account that earns 5% interest each year.  The growth of her investment can be expressed by the exponential equation, A = 4000(1 + .05)^t, where A is the amount in the account after t years.  In how many years will her account exceed $10,000?

• 19 years
• 16 years
• 22 years
• 25 years

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CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.4

The population of a small coastal resort town, currently 3400, grows at a rate of 3% per year.  This growth can be expressed by the exponential equation P = 3400(1+.03)^x, where P is the population after t years.  Find the number of years it will take for the population to reach 10,000?

• 20 years
• 26 years
• 30 years
• 36 years

Tags

CCSS.HSF.LE.A.4