SAT Math Practice Question #736 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #736

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A radioactive isotope decays such that its mass, \( M(t) \), in grams, after \( t \) years is given by the function \( M(t) = M_0 (0.5)^{\frac{t}{h}} \), where \( M_0 \) is the initial mass and \( h \) is the half-life in years. A second radioactive isotope has a half-life that is exactly \( 20\% \) less than that of the first isotope. If both isotopes begin with the exact same initial mass, after how many years will the mass of the first isotope be exactly twice the mass of the second isotope? Express your answer in terms of \( h \).
Select Your Answer:
Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Express the growth/decay rate in factor form: \( A = P(1 \pm r)^t \). Beware whether \( t \) is in years, months, or quarters.

Elimination Framework (Hint 2)

Elimination Shortcut: Check the extremes or test answer choices starting with C to binary search the correct magnitude.

Masterclass Solution & Distractor Trap Analysis

This is a top-tier advanced exponential modeling question. Let's solve it like a master mathematician. Step 1: Define the equations for both isotopes. The mass of the first isotope is \( M_1(t) = M_0 (0.5)^{\frac{t}{h}} \). The half-life of...

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

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