Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A scientist is tracking the population of a certain bacteria. The population doubles every hour. If the initial population is 50 bacteria, which function best models the population P(t) after t hours?
- AP(t) = 50 * 2^t
- BP(t) = 50t^2
- CP(t) = 2 * 50^t
- DP(t) = 50 + 2t
Show answer & explanationAnswer & explanation
Correct answer: A. P(t) = 50 * 2^t
When a quantity doubles at regular intervals, it indicates exponential growth. The general form for exponential growth is P(t) = P₀ * r^t, where P₀ is the initial amount, r is the growth factor (2 for doubling), and t is the number of intervals.
Why the other options are wrong
- B. Incorrect. This represents quadratic growth, which is not appropriate for a doubling phenomenon.
- C. Incorrect. This misplaces the initial population and growth factor, leading to incorrect calculations for exponential growth.
- D. Incorrect. This represents linear growth, where the population increases by a constant amount each hour, not doubling.
Exponential Functions
A function in which the variable appears in the exponent, representing quantities that grow or decay at a constant percentage rate.
- General form: f(x) = a * b^x, where a is initial value, b is growth/decay factor.
- Used to model population growth, compound interest, radioactive decay.
- Graphs show rapid increase or decrease.
Memory trick: Linear, quadratic, exponential: each tells a different story of change.