Exponential Growth And Decay Worksheet Outlet | www ... - Free Printable

Let’s go through each problem one by one. We’ll look at the equation, figure out if it’s growth or decay, find the starting value (initial value), and then find the rate — whether it’s growing or shrinking.

Remember:
- If the number inside the parentheses is greater than 1, it’s exponential growth.
- If the number inside the parentheses is less than 1, it’s exponential decay.
- The initial value is the number multiplied in front of the parentheses.
- The rate is how much it grows or shrinks per step. For growth: subtract 1 from the base. For decay: subtract the base from 1. Then turn that into a percent.

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Problem 1: y = 1200 · (1 + 0.3)^t

A. Is this growth or decay?
→ Inside the parentheses: 1 + 0.3 = 1.3 → which is greater than 1 → Growth

B. Initial value?
→ That’s the number in front: 1200

C. Rate of growth?
→ The “+0.3” means it grows by 0.3 per time unit → 0.3 = 30%

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Problem 2: y = 55 · (1 - 0.02)^t

A. Growth or decay?
→ 1 - 0.02 = 0.98 → less than 1 → Decay

B. Initial value?
→ 55

C. Rate of decay?
→ It’s losing 0.02 per time → 0.02 = 2%

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Problem 3: y = 100 · (1.25)^t

A. Growth or decay?
→ 1.25 > 1 → Growth

B. Initial value?
→ 100

C. Rate of growth?
→ 1.25 - 1 = 0.25 → 25%

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Problem 4: y = 5575 · (0.65)^t

A. Growth or decay?
→ 0.65 < 1 → Decay

B. Initial value?
→ 5575

C. Rate of decay?
→ 1 - 0.65 = 0.35 → 35%

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Problem 5: y = 2000 · (1.05)^t

A. Growth or decay?
→ 1.05 > 1 → Growth

B. Initial value?
→ 2000

C. Rate of growth?
→ 1.05 - 1 = 0.05 → 5%

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Problem 6: y = 14000 · (0.92)^t

A. Growth or decay?
→ 0.92 < 1 → Decay

B. Initial value?
→ 14000

C. Rate of decay?
→ 1 - 0.92 = 0.08 → 8%

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Problem 7: y = 2250 · (1 - 0.9)^t

Wait — let’s simplify inside first: 1 - 0.9 = 0.1

So actually: y = 2250 · (0.1)^t

A. Growth or decay?
→ 0.1 < 1 → Decay

B. Initial value?
→ 2250

C. Rate of decay?
→ 1 - 0.1 = 0.9 → 90%

*(Note: This is a very fast decay — loses 90% each time!)*

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Problem 8: y = 10 · (1 + 0.04)^t

A. Growth or decay?
→ 1 + 0.04 = 1.04 > 1 → Growth

B. Initial value?
→ 10

C. Rate of growth?
→ 0.04 = 4%

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Final Answer:

1. A. Exponential Growth
B. 1200
C. 30%

2. A. Exponential Decay
B. 55
C. 2%

3. A. Exponential Growth
B. 100
C. 25%

4. A. Exponential Decay
B. 5575
C. 35%

5. A. Exponential Growth
B. 2000
C. 5%

6. A. Exponential Decay
B. 14000
C. 8%

7. A. Exponential Decay
B. 2250
C. 90%

8. A. Exponential Growth
B. 10
C. 4%