SAT Math Practice Question #417 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #417

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

A radioactive isotope decays such that its mass, \( M(t) \), in grams, after \( t \) days is modeled 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 days. A sample of Isotope A has a half-life of \( 14 \) days. A sample of Isotope B has a half-life of \( 21 \) days. Initially, the mass of the Isotope A sample is exactly \( 8 \) times the mass of the Isotope B sample. After how many days will the two samples have the exact same mass?
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 question tests your ability to manipulate exponential functions and solve equations with fractional exponents. Let's set up the equations based on the information provided. Let the initial mass of Isotope B be \( M_B \). Then the initi...

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

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