ACT (Enhanced)MathematicsMedium
A chemist is analyzing a reaction where the concentration of a reactant, C, in moles per liter, changes over time t, in seconds, according to the equation C(t) = 0.8e^(-0.15t). What is the initial concentration of the reactant?
- A0.15 mol/L
- B0.65 mol/L
- C0.8 mol/L
- D1.0 mol/L
Show answer & explanationAnswer & explanation
Correct answer: C. 0.8 mol/L
The initial concentration occurs at time t=0. Substituting t=0 into the equation C(t) = 0.8e^(-0.15t) gives C(0) = 0.8e^(0) = 0.8 * 1 = 0.8.
Why the other options are wrong
- A. This is the decay rate constant, not the initial concentration.
- B. This results from an incorrect calculation or misinterpretation of the equation's parameters.
- D. This assumes the initial concentration is 1, which is incorrect for this equation.
Initial Value of Exponential Function
For an exponential function y = ab^x or y = ae^(kx), the initial value is 'a', which is the value of y when x = 0.
- The 'a' term represents the quantity at the start (t=0).
- e^0 = 1, so the exponential term becomes 1 at t=0.
- Finding the initial value involves setting the independent variable to zero.
Memory trick: At 't' zero, 'e' is one, the 'a' coefficient's work is done!