Exponential Growth and Decay Pre-assessment

What is the difference between linear and exponential growth?

• A) Linear growth increases by a constant amount, while exponential growth increases by a constant factor.

• B) Linear growth increases by a constant factor, while exponential growth increases by a constant amount.

• C) Both linear and exponential growth increase by the same pattern.

• Exponential growth always decreases over time.

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TEKS.MATH.9-12.VII.C.1

TEKS.MATH.9-12.IX.B.1

How do you determine whether a sequence is arithmetic or geometric?

• By checking whether the numbers are increasing or decreasing.

• By seeing if the sequence forms a straight line on a graph.

• By looking for a constant difference between terms (arithmetic) or a constant ratio (geometric).

• By adding all the terms together.

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TEKS.MATH.9-12.VII.B

Which of the following scenarios represents an exponential relationship?

• A worker earns $15 per hour.

• A plant grows by 3 inches every week.

• The number of students in a class increases by 2 each year.

• A person deposits $100 in a savings account and earns 5% interest per year.

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TEKS.MATH.9-12.VII.C.2

TEKS.MATH.9-12.VII.C.1

If a sequence starts with 5 and has a common difference of 3, what are the next three terms?

• 10, 15, 20

• 8, 11, 14

• 6, 9, 12

• 15, 18, 21

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CCSS.HSF.BF.A.2

Given the exponential function f(x)=200(1.1)^x, what does the number 200 represent?

• The rate of growth

• The initial amount

• The growth factor

• The exponent

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TEKS.MATH.9-12.VII.C.1

Write an explicit formula for the arithmetic sequence: 4, 7, 10, 13, …

• a_n=4+(n−1)⋅3a

• a_n​=3n−4

• a_n=4n+3a

• a_n=4+3n

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TEKS.MATH.9-12.II.B.1

TEKS.MATH.9-12.VII.C.1

Which graph below represents an exponential function?

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• 
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TEKS.MATH.9-12.VII.A.2

Look at the following table of values. Does it represent an arithmetic or exponential function? Explain.

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TEKS.MATH.9-12.VII.A.2

Describe how you can tell from an equation whether a function is linear or exponential.

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TEKS.MATH.9-12.VII.A.2

Explain why exponential decay occurs in real-world situations. Give an example.

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TEKS.MATH.9-12.VIII.C.2

TEKS.MATH.9-12.X.B.1