GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsHard
A scientist is observing the decay of a radioactive isotope. The graph shows the amount of the isotope remaining (in grams) over time (in days). Which type of function best models this decay process?
- ALogarithmic function
- BQuadratic function
- CExponential decay function
- DLinear function
Show answer & explanationAnswer & explanation
Correct answer: C. Exponential decay function
Radioactive decay, characterized by a constant half-life, means the amount decreases by a fixed percentage over equal time intervals. This pattern is best modeled by an exponential decay function, where the rate of decrease is proportional to the current amount.
Why the other options are wrong
- A. Logarithmic functions typically model growth that slows down over time, or are inverses of exponential functions, not direct decay.
- B. A quadratic function would show a parabolic shape, which is not characteristic of radioactive decay.
- D. A linear function implies a constant amount of decay per unit of time, not a percentage.
Exponential Decay Function
An exponential decay function, typically y = a(b)^x or y = a(1-r)^x, models situations where a quantity decreases by a fixed percentage over equal time intervals.
- 'a' is the initial amount.
- 'b' (or 1-r) is the decay factor, where 'r' is the decay rate as a decimal.
- 'x' (or t) is the number of time periods.
- The decay factor (b) is always between 0 and 1 (0 < b < 1).
Memory trick: Decay is 'E'xponential when it's 'E'very time by a 'P'ercentage!