GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsHard
A researcher is growing a bacterial colony. The number of bacteria, N, after 't' hours, is given by the formula N(t) = 100 * 2^(t/3). How many hours will it take for the colony to reach 800 bacteria?
- A9 hours
- B12 hours
- C6 hours
- D3 hours
Show answer & explanationAnswer & explanation
Correct answer: A. 9 hours
We need to solve 800 = 100 * 2^(t/3) for t. First, divide both sides by 100: 8 = 2^(t/3). We know that 2³ = 8. So, we can set the exponents equal: 3 = t/3. Multiply both sides by 3 to solve for t: t = 3 * 3 = 9 hours.
Why the other options are wrong
- B. This is too high; it might be a result of calculation errors or misinterpreting the exponent.
- C. This might come from incorrectly setting t=6 without solving the exponential properly.
- D. This might come from setting t/3 = 1 (if 2^1=2 was mistakenly used) or an incorrect division.
Solving Exponential Equations (Common Base)
To solve an exponential equation where both sides can be expressed with the same base, rewrite both sides using that common base, then equate the exponents and solve the resulting equation.
- Identify a common base for all terms.
- Rewrite numbers as powers of the common base.
- If b^x = b^y, then x = y.
- Solve the resulting linear or quadratic equation.
Memory trick: Make bases match, then drop them and solve the powers.