GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsHard
A scientist is observing the growth of a bacterial colony. The number of bacteria, N, after 't' hours is given by the equation N = 500 * e^(0.1t). How long will it take for the colony to reach 2000 bacteria? (Use ln(4) ≈ 1.386)
- A10 hours
- B13.86 hours
- C5 hours
- D20 hours
Show answer & explanationAnswer & explanation
Correct answer: B. 13.86 hours
Set N = 2000: 2000 = 500 * e^(0.1t). Divide by 500: 4 = e^(0.1t). Take the natural logarithm of both sides: ln(4) = ln(e^(0.1t)). This simplifies to ln(4) = 0.1t. Using ln(4) ≈ 1.386, we get 1.386 = 0.1t. Divide by 0.1: t = 1.386 / 0.1 = 13.86 hours.
Why the other options are wrong
- A. Incorrect calculation.
- C. Incorrect calculation.
- D. Incorrect calculation.
Solving Exponential Equations (Natural Logarithms)
Solving equations where the variable is in the exponent by using natural logarithms (ln) to bring the exponent down.
- Isolate the exponential term.
- Take the natural logarithm of both sides (ln).
- Use the logarithm property ln(e^x) = x to simplify.
- Solve for the variable.
Memory trick: Exponential out, Logarithm in!