SAT Math Practice Question #865 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #865

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A marine bacterial culture has an initial population of 400 and grows according to the model: \[ P(t) = 400 \cdot (1.21)^{\frac{t}{2}} \] where \( t \) is the time elapsed in hours. By what percentage does the population increase every 1 hours?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Rewrite the exponent to isolate time increments of 1: notice that \( \frac{t}{2} = \left(\frac{t}{1}\right) \cdot \frac{1}{2} \). Apply exponent power rules: \( b^{mn} = (b^m)^n \).

Elimination Framework (Hint 2)

Desmos Shortcut: In Desmos, define \( P(t) = 400(1.21)^{t/2} \). Then simply calculate \( \frac{P(1) - P(0)}{P(0)} \cdot 100 \). Desmos gives the exact percentage instantly!

Masterclass Solution & Distractor Trap Analysis

To determine the growth rate every 1 hours, evaluate the factor by which the population multiplies when \( t \) increases by 1: \[ \text{Growth Multiplier} = (1.21)^{\frac{1}{2}} = (1.21)^{\frac{1}{2}} = \sqrt{1.21} = 1.10 \] A multiplier o...

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

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