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5.01 Exponential patterns and sequences

Adaptive
Worksheet

Interactive practice questions

Consider the pattern.

A pattern of black circles with green outlines is arranged in steps. The first step, labeled "Step $1$1," consists of $4$4 circles arranged in a small cluster. The second step, labeled "Step $2$2," consists of $12$12 circles arranged in a larger cluster. The third step, labeled "Step $3$3," consists of $36$36 circles arranged in a more complex pattern.
a

How could we describe the pattern?

Dividing by $3$3

A

Adding $4$4

B

Multiplying by $4$4

C

Multiplying by $3$3

D
b

How many circles will the next step in the pattern contain?

Easy
1 min

Consider the pattern.

Easy
1 min

Consider the pattern.

Easy
1 min

Consider the pattern.

Easy
1 min
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Outcomes

A1.F.IF.B.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate and interpret the rate of change from a graph.*

A1.F.BF.A.1

Build a function that describes a relationship between two quantities.*

A1.F.BF.A.1.A

Determine steps for calculation, a recursive process, or an explicit expression from a context.

A1.F.LE.A.1.A

Know that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.

A1.F.LE.A.1.C

Recognize situations in which a quantity grows or decays by a constant factor per unit interval relative to another.

A1.MP1

Make sense of problems and persevere in solving them.

A1.MP2

Reason abstractly and quantitatively.

A1.MP3

Construct viable arguments and critique the reasoning of others.

A1.MP4

Model with mathematics.

A1.MP6

Attend to precision.

A1.MP7

Look for and make use of structure.

A1.MP8

Look for and express regularity in repeated reasoning.

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