Exponential Growth and Decay Word Problems worksheet with five real-world math problems.

Let’s solve each problem one by one. I’ll show my work step by step so you can follow along easily.

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Problem 1:

> In 2004, there were 350 people at the annual town fair. Each year, the number of people has increased by 12%. How many people will be at the fair in 2024?

We’re dealing with exponential growth here. The formula is:

> Final amount = Initial amount × (1 + rate)^time

- Initial amount = 350
- Rate = 12% = 0.12
- Time = 2024 - 2004 = 20 years

So:

Final = 350 × (1.12)^20

Let me calculate (1.12)^20 first.

Using a calculator:
(1.12)^20 ≈ 9.6463

Now multiply:

350 × 9.6463 ≈ 3376.205

Since we can’t have a fraction of a person, round to nearest whole number → 3376

✔ Check: Growth over 20 years at 12% per year should be large — yes, from 350 to ~3376 makes sense.

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Problem 2:

> In 2008, there were 200 girls who attended the local dance recital. The number of girls increased by 15% each year after that. How many girls attended the recital in 2018?

Again, exponential growth.

- Initial = 200
- Rate = 15% = 0.15
- Time = 2018 - 2008 = 10 years

Formula: Final = 200 × (1.15)^10

Calculate (1.15)^10:

≈ 4.0456

Then:

200 × 4.0456 ≈ 809.12 → Round to 809

✔ Check: 15% growth for 10 years — doubling roughly every 5 years? 200 → 400 → 800 — yes, 809 fits.

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Problem 3:

> Bacteria are multiplying at an alarming rate and spread quickly across the city. At midnight, if you start with 10 bacteria cells, how many bacteria cells will you have after 6 hours if they double every hour?

This is doubling every hour, so it’s exponential with base 2.

Start: 10 cells
After 1 hour: 10 × 2 = 20
After 2 hours: 20 × 2 = 40
... or use formula: Final = Initial × 2^time

Time = 6 hours

Final = 10 × 2^6 = 10 × 64 = 640

✔ Check: 2^6 = 64, times 10 = 640 — correct.

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Problem 4:

> Last year your favorite music festival had 1,000 attendees. This year, attendance grew by 25%. Next year, it’s expected to grow by another 25%. What will the attendance be next year?

Two consecutive 25% increases.

First year (this year):
1000 × 1.25 = 1250

Next year:
1250 × 1.25 = ?

1250 × 1.25 = 1250 × 5/4 = (1250 ÷ 4) × 5 = 312.5 × 5 = 1562.5 → Round to 1563

Or directly: 1000 × (1.25)^2 = 1000 × 1.5625 = 1562.5 → 1563

✔ Check: 25% twice is not 50% total — it’s compounding, so more than 1500 — yes, 1563 is right.

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Problem 5:

> The population of a small town was 5,000 in 2010. It grows at a rate of 3% per year. What will the population be in 2025?

Exponential growth again.

Initial = 5000
Rate = 3% = 0.03
Time = 2025 - 2010 = 15 years

Final = 5000 × (1.03)^15

Calculate (1.03)^15:

≈ 1.55797

Then:

5000 × 1.55797 ≈ 7789.85 → Round to 7790

✔ Check: 3% per year for 15 years — slow but steady growth — from 5000 to ~7790 seems reasonable.

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Problem 6:

> Your grandmother started saving money in 1980 with $100. She earned 5% interest each year, compounded annually. How much money will she have in 2025?

Compound interest — same as exponential growth.

Initial = $100
Rate = 5% = 0.05
Time = 2025 - 1980 = 45 years

Final = 100 × (1.05)^45

Calculate (1.05)^45:

≈ 8.985

Then:

100 × 8.985 = 898.50

✔ Check: 5% for 45 years — Rule of 72 says doubles every ~14.4 years → 45 / 14.4 ≈ 3.1 doublings → 100 → 200 → 400 → 800 — close to 898.50 — good.

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Problem 7:

> During winter break, 200 students went on a trip to visit a national park. After returning home, each student told 3 friends about the trip. Those friends then each told 3 more friends, and this continued for 4 rounds. How many total people heard about the trip after 4 rounds?

This is a geometric series — each round, the number of new people triples.

But note: “total people” includes all who heard — original 200 + those told in round 1 + round 2 + round 3 + round 4.

Round 0: 200 (original)

Round 1: 200 × 3 = 600 new → Total so far: 200 + 600 = 800

Round 2: 600 × 3 = 1800 new → Total: 800 + 1800 = 2600

Round 3: 1800 × 3 = 5400 new → Total: 2600 + 5400 = 8000

Round 4: 5400 × 3 = 16200 new → Total: 8000 + 16200 = 24200

Alternatively, use geometric series sum:

Total = 200 + 200×3 + 200×3² + 200×3³ + 200×3⁴

= 200 × (1 + 3 + 9 + 27 + 81) = 200 × 121 = 24200

✔ Check: Sum of powers of 3 up to 3^4: 1+3=4, +9=13, +27=40, +81=121 → 200×121=24200 — correct.

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Final Answer:
1. 3376
2. 809
3. 640
4. 1563
5. 7790
6. 898.50
7. 24200