GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A scientist is observing the growth of a bacterial colony. The number of bacteria (N) after 't' hours can be modeled by N(t) = 50 * 2^(t/3). How many hours will it take for the number of bacteria to reach 800?
- A15 hours
- B6 hours
- C9 hours
- D12 hours
Show answer & explanationAnswer & explanation
Correct answer: D. 12 hours
This problem requires solving an exponential equation. We need to isolate the exponential term, then use logarithms to solve for the exponent.
Why the other options are wrong
- A. At 15 hours, N(15) = 50 * 2^(15/3) = 50 * 2^5 = 50 * 32 = 1600, which is incorrect.
- B. At 6 hours, N(6) = 50 * 2^(6/3) = 50 * 2^2 = 50 * 4 = 200, which is incorrect.
- C. At 9 hours, N(9) = 50 * 2^(9/3) = 50 * 2^3 = 50 * 8 = 400, which is incorrect.
Solving Exponential Equations (Logarithms for Variable in Exponent)
Equations where the variable appears in the exponent. Solved by isolating the exponential term and then applying logarithms to both sides to bring the exponent down.
- Isolate the exponential term first.
- Take the logarithm (natural log or common log) of both sides.
- Use the logarithm property log(b^x) = x log(b) to bring down the exponent.
- Solve the resulting linear equation for the variable.
Memory trick: Logarithms Level Exponents.