Digital SATMath: AlgebraEasy
The number of bacteria in a culture doubles every hour. If there are initially 50 bacteria, which equation represents the number of bacteria, N, after t hours?
- AN = 50 * t^2
- BN = 50 * 2^t
- CN = 50 + 2t
- DN = 2 * 50^t
Show answer & explanationAnswer & explanation
Correct answer: B. N = 50 * 2^t
This is an exponential growth scenario. The initial amount is 50, and it doubles (multiplies by 2) for every hour (t). So the number of bacteria N after t hours is given by the initial amount times the growth factor raised to the power of time: N = 50 * 2^t.
Why the other options are wrong
- A. This is a quadratic model. Doubling implies multiplication by a factor, not raising time to a power. Incorrect model.
- C. This represents linear growth, where 2 bacteria are added each hour, not doubled. Incorrect model.
- D. This incorrectly places the initial amount as the base and the growth factor as the coefficient. Incorrect exponential form.
Exponential Growth Model
An exponential growth model describes a quantity that increases at a rate proportional to its current value. It is represented by the formula y = a * b^x, where 'a' is the initial amount, 'b' is the growth factor (b > 1), and 'x' is the number of growth periods.
- Growth factor 'b' is (1 + rate of increase).
- The variable representing time or periods is in the exponent.
- Commonly used for population growth, compound interest, and radioactive decay (decay when b < 1).
Memory trick: Exponent's power: small changes grow big, fast!