SAT Math Practice Question #1159 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #1159

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

For a certain exponential growth model \( P(t) = C \cdot (1.25)^{\frac{t}{6}} \), where \( t \) represents the number of hours elapsed, by what percent does \( P(t) \) increase every 24 hours?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Rewrite the exponent t/6 when t = 24. Calculate the 24-hour factor (1.25)^4 and subtract 1 to get the percentage increase.

Elimination Framework (Hint 2)

Desmos Shortcut: Enter 1.25^4 in Desmos. It outputs 2.441406. Subtract 1 to see the increase: 1.4414 = 144.1%.

Masterclass Solution & Distractor Trap Analysis

To find the growth over 24 hours, substitute t = 24 into the growth factor: (1.25)^(24/6) = (1.25)^4. Calculate 1.25^4: 1.25^2 = 1.5625; 1.5625^2 ≈ 2.4414. A multiplier of 2.4414 corresponds to an increase of (2.4414 - 1) * 100% = 144.14%. ...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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