GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A scientist is observing the decay of a radioactive isotope. The amount of the isotope remaining, A(t), in grams, after t hours, is given by the function A(t) = 500(0.8)^t. What does the number 0.8 represent in this context?
- AThe decay factor per hour.
- BThe amount decayed per hour.
- CThe number of hours elapsed.
- DThe initial amount of the isotope.
Show answer & explanationAnswer & explanation
Correct answer: A. The decay factor per hour.
In an exponential decay function of the form y = a(b)^x, 'b' is the decay factor. Here, 0.8 is the base of the exponent, which represents the factor by which the isotope amount is multiplied each hour, indicating it's the decay factor. This decay factor (0.8) implies a 20% decay rate per hour (1 - 0.8 = 0.20).
Why the other options are wrong
- B. The amount decayed is 20% (0.2) of the current amount each hour, not a fixed amount.
- C. The number of hours is represented by 't', the independent variable in the exponent.
- D. The initial amount is represented by 'a', which is 500 grams in this equation.
Exponential Decay Function Components
An exponential decay function y = a(b)^x models situations where a quantity decreases by a constant percentage over time. 'a' is the initial value, 'b' is the decay factor (1 - rate), and 'x' is the time.
- a = initial amount.
- b = decay factor (0 < b < 1 for decay).
- b = 1 - r, where r is the decay rate as a decimal.
Memory trick: A is start, B is factor, X is time's power.