GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A chemist is studying the decay of a certain radioactive isotope. The remaining amount, A, in grams, after 't' hours is given by the formula A = A₀ * (1/2)^(t/h), where A₀ is the initial amount and 'h' is the half-life in hours. If the initial amount is 200 grams and the half-life is 5 hours, how much of the isotope remains after 15 hours?
- A25 grams
- B6.25 grams
- C50 grams
- D12.5 grams
Show answer & explanationAnswer & explanation
Correct answer: A. 25 grams
Substitute A₀ = 200, h = 5, and t = 15 into the formula: A = 200 * (1/2)^(15/5) = 200 * (1/2)³ = 200 * (1/8) = 25 grams.
Why the other options are wrong
- B. Incorrect calculation (e.g., 200 * (1/32)).
- C. Incorrect calculation (e.g., 200 * (1/4)).
- D. Incorrect calculation (e.g., 200 * (1/16)).
Evaluating Exponential Functions (Half-Life)
Calculating the value of an exponential function at a specific point, often used in scenarios like radioactive decay where a quantity decreases by a fixed factor over equal time intervals (half-life).
- Identify the base (often 1/2 for half-life) and the exponent.
- Substitute the given values for variables into the function.
- Perform the exponentiation first, then multiplication.
Memory trick: Plug and Chug, then Watch it grow/shrink!