CMClearMathAcademy

Exponential Functions and Sequences Checkpoint

A free Algebra I lesson from the “Exponential Functions and Sequences” unit, with a worked example and practice problems including step-by-step solutions.

This checkpoint reviews exponential growth, exponential decay, arithmetic sequences, geometric sequences, and the decision-making needed to tell linear and exponential patterns apart. In Exponential Functions and Sequences, students need more than a memorized rule: they need to recognize the structure, select a method, carry out the algebra cleanly, and interpret the answer in a graph, table, equation, or real context. The expanded practice now mixes skill fluency, transfer questions, and cumulative review so the lesson builds durable Algebra I readiness.

What you'll learn

Why it matters: Algebra I assessments mix symbolic fluency with modeling, graph interpretation, and strategy choice so students practice the same switching they need on cumulative tests.

Worked example

Problem. Worked example from Exponential Functions: If f(x) = 5 * 3^x, find f(0).

  1. Warm-up: First identify exactly what the question is asking: If f(x) = 5 * 3^x, find f(0).
  2. For function notation, treat the value inside parentheses as the input and carefully substitute it into the rule.
  3. 3^0 = 1, so f(0) = 5 * 1 = 5.
  4. Check the result by substituting or estimating: the response should match 5 and make sense in the original problem.

Answer: 5

Practice problems

1. Exponential Functions and Sequences Checkpoint review case A from Exponential Functions: If f(x) = 5 * 3^x, find f(0).

Show solution
  1. Warm-up: First identify exactly what the question is asking: If f(x) = 5 * 3^x, find f(0).
  2. For function notation, treat the value inside parentheses as the input and carefully substitute it into the rule.
  3. 3^0 = 1, so f(0) = 5 * 1 = 5.
  4. Check the result by substituting or estimating: the response should match 5 and make sense in the original problem.
  5. Identify the Algebra I structure before choosing a calculation.

Answer: 5

2. Exponential Functions and Sequences Checkpoint review case B from Exponential Functions: If f(x) = 5 * 3^x, find f(2).

Show solution
  1. Warm-up: First identify exactly what the question is asking: If f(x) = 5 * 3^x, find f(2).
  2. For function notation, treat the value inside parentheses as the input and carefully substitute it into the rule.
  3. 3^2 = 9, so f(2) = 5 * 9 = 45.
  4. Check the result by substituting or estimating: the response should match 45 and make sense in the original problem.
  5. Identify the Algebra I structure before choosing a calculation.

Answer: 45

3. Exponential Functions and Sequences Checkpoint review case C from Exponential Functions: If f(x) = 2 * 4^x, find f(1).

Show solution
  1. Warm-up: First identify exactly what the question is asking: If f(x) = 2 * 4^x, find f(1).
  2. For function notation, treat the value inside parentheses as the input and carefully substitute it into the rule.
  3. f(1) = 2 * 4 = 8.
  4. Check the result by substituting or estimating: the response should match 8 and make sense in the original problem.
  5. Identify the Algebra I structure before choosing a calculation.

Answer: 8

4. Exponential Functions and Sequences Checkpoint review case D from Exponential Functions: For y = 100 * (1.05)^x, enter the initial value.

Show solution
  1. Core Practice: First identify exactly what the question is asking: For y = 100 * (1.05)^x, enter the initial value.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. The initial value is the a in y = a * b^x.
  4. Here a = 100.
  5. Check the result by substituting or estimating: the response should match 100 and make sense in the original problem.

Answer: 100

5. Exponential Functions and Sequences Checkpoint review case E from Exponential Functions: For y = 100 * (1.05)^x, enter the growth factor.

Show solution
  1. Core Practice: First identify exactly what the question is asking: For y = 100 * (1.05)^x, enter the growth factor.
  2. Use the structure of the expression to choose a factoring pattern, then check that the factors multiply back to the original expression.
  3. The growth factor is the b in y = a * b^x.
  4. Here b = 1.05.
  5. Check the result by substituting or estimating: the response should match 1.05 and make sense in the original problem.

Answer: 1.05

Practice this interactively with instant feedback and an AI tutor.

Practice Exponential Functions and Sequences Checkpoint Take the free placement check

More Algebra I lessons