GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsEasy
A scientist is observing the growth of a bacterial colony. The number of bacteria (N) after 't' hours is given by the function N(t) = 500 * (1.08)^t. How many bacteria will there be after 5 hours?
- A734
- B500
- C540
- D760
Show answer & explanationAnswer & explanation
Correct answer: A. 734
To find the number of bacteria after 5 hours, substitute t=5 into the function: N(5) = 500 * (1.08)^5. Calculate (1.08)^5 ≈ 1.4693. Then, N(5) = 500 * 1.4693 = 734.65. Rounding to the nearest whole number of bacteria, we get 734.
Why the other options are wrong
- B. This is the initial population at t=0, not after 5 hours.
- C. This would be 500 * 1.08 = 540, which is the population after 1 hour, not 5 hours.
- D. This is an incorrect calculation, possibly from rounding too early or a miscalculation of the exponent.
Evaluating Exponential Functions (Growth)
Determining the value of a quantity at a specific point in time using an exponential growth function, where the quantity increases by a fixed percentage over regular intervals.
- General form: A(t) = P(1 + r)^t, where P is initial amount, r is growth rate, t is time.
- Substitute the given time value for 't'.
- Calculate the exponent first, then multiply by the initial amount.
Memory trick: Exponential Growth: Start, then grow by the rate, 't' times!