Writing Exponential Functions from Word Problems

A particular type of cell triples in number every hour. Which function can be used to find the number of cells present at the end of h hours if there are initially 6 of these cells?

• f(h) = 3(6)^h

• f(h) = 6x^h

• f(h) = 6(3)^h

• f(h) = 3(6h)

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CCSS.HSF.BF.A.1

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CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

The amount of cola in a soda machine decreases by a rate of 5% each hour. The amount of cola in the machine was originally 75 gallons.

Which function models the amount of cola in gallons after h hours?

• f(h) = 75(-5)^h

• f(h) = -5(75)^h

• f(h) = .95(75)^h

• f(h) = 75(.95)^h

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CCSS.HSF.BF.A.1

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Write an exponential function to model the situation. Then solve.

The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year. Which equations represents this situation?

• C(t) = 1.06(12000)^t

• C(t) = 12000(.06)^t

• C(t) = 12000(.06)^t

• C(t) = 12000(1.06)^t

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CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

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CCSS.HSF.LE.B.5

Write an exponential function to model the situation. You invest $1500. Your investment increases at a rate of 3.5%.

• B(t) = 1500(0.965)^t

• B(t) = 1500(1.035)^t

• B(t) = 1500(.035)^t

• B(t) = 1500(1.965)^t

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CCSS.HSA.SSE.A.1

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Write an exponential function to model the situation. The value of a car is $18000 and is depreciating at a rate of 12% per year.

• V(t) = .88(18000)^t

• V(t) = .12(18000)^t

• V(t) = 18000(.88)^t

• V(t) = 18000(.12)^t

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CCSS.HSA.CED.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

What is the a-value (or y-intercept) for the function: f(x) = 800(0.85)^x?

• 800

• 0.85

• 0.15

• x

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CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.4

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

• y = 8(15,000)^x

• y = 15,000(1.08)^x

• y = 15,000(0.92)^x

• y = 15,000(0.08)^x

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CCSS.HSA.CED.A.1

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The equation f(x) = 300(1.06)^x is being used to calculate the amount of money in a savings account.  What does the 1.06 represent?

• 6% growth
• 6% decay
• 1.06% growth
• .06% decay

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CCSS.HSA.SSE.A.1

CCSS.HSF.LE.B.5

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

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CCSS.HSF.BF.A.1

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Determine if the equation y = 15(1.35)^x represents exponential growth or decay and justify. Hint: Think about the growth and decay equations.

• Growth, because the scale factor is greater than 1

• Growth, because the scale factor is less than 1

• Decay, because the scale factor is greater than 1

• Decay, because the scale factor is less than 1

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CCSS.HSF.LE.A.1

CCSS.HSF.LE.B.5