GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A scientist is observing the decay of a radioactive substance. The amount of the substance remaining, A(t), in grams, after t days, is given by the graph below. According to the graph, what is the half-life of the substance?
- A4 days
- B6 days
- C2 days
- D8 days
Show answer & explanationAnswer & explanation
Correct answer: A. 4 days
The half-life is the time it takes for half of the substance to decay. Find the initial amount, then find half of that amount. Trace from that half-amount on the y-axis to the graph, then down to the x-axis to find the corresponding time.
Why the other options are wrong
- B. This is incorrect; at 6 days, the amount is 5 grams, which is a quarter of the initial amount.
- C. This is incorrect; at 2 days, the amount is 10 grams, which is not half of 20.
- D. This is incorrect; at 8 days, the amount is 2.5 grams, which is an eighth of the initial amount.
Interpreting Half-Life from a Graph
The half-life of a substance is the time required for half of the initial amount of the substance to undergo decay. On a decay graph, it's the time taken for the amount to drop to 50% of its initial value.
- Find initial amount (y-intercept).
- Calculate half of the initial amount.
- Locate this half-amount on the y-axis.
- Trace horizontally to the graph, then vertically down to the x-axis to find the time.
Memory trick: Start Amount, Halve It, Find the Time!