Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A chemist is observing a reaction where the concentration of a certain substance decreases over time. The concentration C(t) in milligrams per liter after t hours is modeled by C(t) = 150 * (0.8)^t. What is the initial concentration of the substance?
- A1.5 mg/L
- B120 mg/L
- C150 mg/L
- D0.8 mg/L
Show answer & explanationAnswer & explanation
Correct answer: C. 150 mg/L
In an exponential function of the form C(t) = C_0 * (b)^t, C_0 represents the initial value (when t=0). In this equation, C_0 is 150.
Why the other options are wrong
- A. Incorrect. This is 1/100th of the initial concentration.
- B. Incorrect. This would be the concentration after 1 hour (150 * 0.8).
- D. Incorrect. This is the decay factor.
Initial Value of Exponential Function
The starting amount or quantity of a substance or value at the beginning of a process, represented by the coefficient in an exponential model.
- Found when the exponent (time) is zero.
- In P(t) = P_0 * b^t, P_0 is the initial value.
- Represents the y-intercept on a graph.
Memory trick: Initial is 'I' for 'Isolated coefficient' – the number standing alone, multiplying the power.