GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsHard
A chemist is observing a reaction where the amount of reactant, R, in grams, remaining after 't' minutes is modeled by the equation R(t) = 100 * (0.8)^t. How many minutes will it take for the amount of reactant to be 64 grams?
- A3 minutes
- B1 minute
- C2 minutes
- D4 minutes
Show answer & explanationAnswer & explanation
Correct answer: C. 2 minutes
Substitute R(t) = 64 into the equation: 64 = 100 * (0.8)^t. Divide both sides by 100: 64/100 = (0.8)^t, which simplifies to 0.64 = (0.8)^t. Recognize that 0.64 is equal to (0.8)^2. Therefore, (0.8)^2 = (0.8)^t, which implies t = 2 minutes.
Why the other options are wrong
- A. This would result in R(3) = 100 * (0.8)^3 = 100 * 0.512 = 51.2 grams, not 64.
- B. This would result in R(1) = 100 * 0.8 = 80 grams, not 64.
- D. This would result in R(4) = 100 * (0.8)^4 = 100 * 0.4096 = 40.96 grams, not 64.
Solving Exponential Equations (Common Base)
Solving an exponential equation by rewriting both sides with the same base, then equating the exponents.
- Try to express both sides with a common base.
- If bases are equal, exponents must be equal.
- May require recognizing powers of numbers.
Memory trick: Match the Bases: Make them the same, then drop 'em!