DOK 3 Practice

Justify model choices and critique exponential reasoning.

These questions ask students to explain why a model fits, analyze errors, and compare representations.

How to use this set

For analysis questions, answer the why: constant ratio, growth factor, decay factor, or eventual exponential growth.

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Set Focus

Exponential analysis and justification

DOK 3 questions reward precise evidence from tables, equations, graphs, and contexts.

Justification

Defend exponential choices with equal-factor reasoning.

Error analysis

Correct common mix-ups between addition and multiplication.

Comparison

Compare linear and exponential models over time.

Interpretation

Explain parameters and sequence connections.

Practice Questions

Analysis and Model Choice

Check your answer first, then reveal the explanation when you want the model.

Question 1

Justify model choice

A table shows y-values 8, 12, 18, 27 for equal x-steps. What is the best justification for an exponential model?

Question 2

Error analysis

A student writes y=9+2x for a pattern that starts at 9 and doubles each step. What correction should be made?

Question 3

Compare growth

Function A is A(x)=10+6x. Function B is B(x)=10(1.5)^x. Which statement is true?

Question 4

Representation choice

Which situation is best modeled by an exponential function?

Question 5

Analyze a table

Use the table to decide which model fits best.

Observed values

x	0	1	2	3
y	2	5	12.5	31.25

Question 6

Parameter meaning

The model R(d)=1200(0.6)^d gives a lake's remaining algae after treatment day d. Which interpretation is strongest?

Question 7

Sequence connection

A sequence is defined by a_1=3 and a_n=2a_{n-1}. Which statement connects it to functions?

Question 8

Compare later values

At x=0, two functions both have value 5. Function L adds 4 each step. Function E doubles each step. Which statement is most reasonable?

Question 9

Graph interpretation

A graph shows points (0,16), (1,8), (2,4), and (3,2). Which model is most likely?

Decay pattern

Question 10

Critique a claim

A student says y=4(3)^x and y=4+3x are the same because both use 4 and 3. What is the best response?

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