DOK 2 Practice

Apply exponential thinking to tables, contexts, and rules.

This set asks students to write, interpret, and compare exponential models from common Math 1 representations.

How to use this set

Start by identifying the starting value and the repeated factor. Then decide whether the model is growth, decay, or a linear comparison.

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Set Focus

Applied exponential reasoning

DOK 2 questions usually require a representation switch before the calculation.

Contexts

Turn percent change, doubling, and decay language into equations.

Tables

Read initial values and common ratios from rows.

Sequences

Connect geometric sequences with exponential rules.

Technology checks

Use substitution or graphing to verify points.

Practice Questions

Applications and Model Writing

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

Question 1

Model type

A savings account starts with \$200 and grows by 5% each year. Which model type fits best?

Question 2

Write a rule

A plant is 6 inches tall and triples in height each week. Which function models height h after w weeks?

Question 3

Table to equation

Which equation matches the table?

Function values

x	0	1	2	3
y	4	12	36	108

Question 4

Interpret factor

The function P(t)=500(0.8)^t models a population after t years. What does 0.8 mean?

Question 5

Compare patterns

Function A has y-values 10, 15, 20, 25. Function B has y-values 10, 15, 22.5, 33.75. Which statement is true for equal x-steps?

Question 6

Geometric sequence

A geometric sequence has first term 5 and common ratio 4. Which explicit rule gives term n?

Question 7

Evaluate context

A rumor reaches 3 students first. Each round, the number of students who hear it doubles. How many students have heard it after 4 rounds?

Question 8

Recursive rule

Which recursive rule matches the sequence 2, 10, 50, 250, ...?

Question 9

Choose an equation

A car worth \$18{,}000 loses 12% of its value each year. Which model gives value V after t years?

Question 10

Technology check

A student graphs y=2(3)^x. Which point should appear on the graph?

Desmos tip: graph the equation and test choices by entering the ordered pairs or substituting the x-value.

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