Word Problems on Exponents
Exponents appear in real life wherever quantities grow by repeated multiplication — population growth, bacteria doubling, computer memory, and very large or small numbers in science.
Word problems on exponents require you to identify the base and exponent from the problem context and apply exponent rules to find the answer.
What is Word Problems on Exponents - Grade 7 Maths (Exponents and Powers)?
Key concepts:
- Doubling: Something doubles n times = multiply by 2n.
- Tripling: Something triples n times = multiply by 3n.
- Powers of 10: Large numbers like millions (106) and billions (109).
Word Problems on Exponents Formula
Common patterns:
After n doublings: original × 2n
Types and Properties
Common problem types:
- Bacteria/cell division: Population doubles every hour.
- Computer storage: Memory in powers of 2 (KB, MB, GB).
- Large numbers: Expressing and comparing using standard form.
- Paper folding: Thickness doubles with each fold.
Solved Examples
Example 1: Bacteria Growth
Problem: A bacteria culture starts with 1 cell and doubles every hour. How many cells after 10 hours?
Solution:
- After 10 hours = 1 × 210 = 1024 cells
Answer: 1024 cells.
Example 2: Computer Memory
Problem: 1 KB = 210 bytes. How many bytes is 1 KB?
Solution:
- 210 = 1024 bytes
Answer: 1024 bytes.
Example 3: Paper Folding
Problem: A piece of paper is 0.1 mm thick. After folding it 7 times, what is the thickness?
Solution:
- Each fold doubles the thickness.
- After 7 folds: 0.1 × 27 = 0.1 × 128 = 12.8 mm
Answer: 12.8 mm.
Example 4: Comparing Large Numbers
Problem: Which is larger: 38 or 83?
Solution:
- 38 = 6561
- 83 = 512
Answer: 38 is larger.
Real-World Applications
Real-world uses:
- Biology: Cell division, virus spread.
- Technology: Data storage (210 = 1 KB, 220 = 1 MB).
- Finance: Compound growth over time.
- Science: Very large numbers (distance to stars) and very small numbers (size of atoms).
Key Points to Remember
- Doubling n times = multiply by 2n.
- Powers of 10 are used for large numbers in science.
- Use laws of exponents to simplify calculations.
- Always check: is the growth repeated multiplication (use exponents) or repeated addition (use multiplication)?
Practice Problems
- A lily pad doubles in area every day. After 20 days it covers a whole pond. On which day did it cover half?
- Find 5⁴ × 5³.
- Express 1 GB in bytes using powers of 2 (1 GB = 2³⁰ bytes).
- A virus triples every hour starting from 100. How many after 4 hours?
Frequently Asked Questions
Q1. When do you use exponents in word problems?
When a quantity grows by repeated multiplication (doubling, tripling), or when dealing with very large/small numbers that use powers of 10.
Q2. What does 'doubles every hour' mean mathematically?
After n hours, the quantity = original × 2ⁿ. Doubling is multiplication by 2 each time.
Q3. How is 1 MB related to bytes?
1 MB = 2²⁰ bytes = 1,048,576 bytes (approximately 1 million bytes).
