Modeling Repeated Doubling with Exponents
This Grade 7 math skill from Reveal Math, Accelerated introduces students to modeling repeated doubling with exponents. Students learn how quantities that double repeatedly—such as bacteria growth or folding paper—can be expressed compactly using exponential notation, building a foundation for understanding exponential growth.
Key Concepts
Property When a quantity doubles repeatedly, its exponential growth can be modeled using the expression: $$\text{Final Value} = \text{Initial Value} \cdot 2^n$$ where $n$ is the number of times the quantity doubles.
Examples Example 1 (Bacteria): A bacteria population starts with 50 cells and doubles every hour. After 4 hours, the population is $50 \cdot 2^4 = 50 \cdot 16 = 800$ cells.
Example 2 (Paper Folding): A piece of paper is 0.1 mm thick. After $n$ folds, its thickness is $0.1 \cdot 2^n$. How many folds are needed to exceed 100 mm?
Common Questions
What does repeated doubling mean in math?
Repeated doubling means multiplying a quantity by 2 again and again. For example, starting with 1 and doubling three times gives 1, 2, 4, 8, which equals 2 to the power of 3.
How are exponents used to model repeated doubling?
If a value doubles n times starting from an initial value a, the result is a × 2^n. Exponents provide a compact way to express many repeated multiplications.
What is a real-world example of repeated doubling?
Bacteria populations that double every hour can be modeled with exponents: after t hours, the population is initial count × 2^t.
What is the difference between exponential and linear growth?
Linear growth adds a constant amount each step, while exponential growth multiplies by a constant. Doubling is a classic example of exponential growth.
Where is this skill covered in Reveal Math Accelerated?
Modeling repeated doubling with exponents is taught in the Grade 7 Reveal Math, Accelerated textbook.