FOCUSED PRACTICE

SAT exponential growth practice

Distinguish multiplying by a factor from adding a fixed amount, then interpret the model in context.

The idea to remember

For y = a(b)ˣ, a is the starting value and b is the factor per step. A 20% increase means b = 1.20, not 0.20.

A worked example

A model P = 100(1.2)ᵗ gives P = 144 after two steps because 100 × 1.2 × 1.2 = 144. Adding 20 twice would incorrectly give 140.

A common trap

The growth factor includes the original 100%. A decay of 15% keeps 85%, giving a factor of 0.85.

For a longer walkthrough, read Read SAT tables, slopes, and growth models with confidence.

By Graph Math Practice editorial team · Reviewed 2026-09-05

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All 8 questions, with explanations

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1. A population is modeled by P(t) = 80(1.5)ᵗ. What is the population predicted by this model when t = 2?
1. 180
2. 160
3. 120
4. 240
Show answer and explanation
Answer: A. 180
Substitute t = 2: P(2) = 80 × 1.5² = 80 × 2.25 = 180. Apply the multiplier twice. Doubling the initial value would represent a different model.
2. A machine has value V(t) = 8000(0.9)ᵗ dollars after t years. By what percent does its value decrease each year?
1. 90%
2. 15%
3. 20%
4. 10%
Show answer and explanation
Answer: D. 10%
The factor 0.9 means the machine keeps 90% of its value each year. The decrease is 100% - 90% = 10%. The initial value does not determine the percentage decrease.
3. A population is modeled by P(t) = 120(1.5)ᵗ. What is the population predicted by this model when t = 2?
1. 180
2. 360
3. 270
4. 240
Show answer and explanation
Answer: C. 270
Substitute t = 2: P(2) = 120 × 1.5² = 120 × 2.25 = 270. Apply the multiplier twice. Doubling the initial value would represent a different model.
4. A machine has value V(t) = 12000(0.85)ᵗ dollars after t years. By what percent does its value decrease each year?
1. 30%
2. 15%
3. 85%
4. 20%
Show answer and explanation
Answer: B. 15%
The factor 0.85 means the machine keeps 85% of its value each year. The decrease is 100% - 85% = 15%. The initial value does not determine the percentage decrease.
5. A population is modeled by P(t) = 160(1.5)ᵗ. What is the population predicted by this model when t = 2?
1. 360
2. 320
3. 240
4. 480
Show answer and explanation
Answer: A. 360
Substitute t = 2: P(2) = 160 × 1.5² = 160 × 2.25 = 360. Apply the multiplier twice. Doubling the initial value would represent a different model.
6. A machine has value V(t) = 16000(0.8)ᵗ dollars after t years. By what percent does its value decrease each year?
1. 80%
2. 25%
3. 40%
4. 20%
Show answer and explanation
Answer: D. 20%
The factor 0.8 means the machine keeps 80% of its value each year. The decrease is 100% - 80% = 20%. The initial value does not determine the percentage decrease.
7. A population is modeled by P(t) = 200(1.5)ᵗ. What is the population predicted by this model when t = 2?
1. 300
2. 600
3. 450
4. 400
Show answer and explanation
Answer: C. 450
Substitute t = 2: P(2) = 200 × 1.5² = 200 × 2.25 = 450. Apply the multiplier twice. Doubling the initial value would represent a different model.
8. A machine has value V(t) = 20000(0.75)ᵗ dollars after t years. By what percent does its value decrease each year?
1. 50%
2. 25%
3. 75%
4. 30%
Show answer and explanation
Answer: B. 25%
The factor 0.75 means the machine keeps 75% of its value each year. The decrease is 100% - 75% = 25%. The initial value does not determine the percentage decrease.

Scope reference: College Board’s section overview. Questions are independently authored and are not official exam material.

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