GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A chemist is observing a chemical reaction where the concentration of a certain substance, C, in moles per liter, changes over time, t, in minutes, according to the function C(t) = 0.5e^(-0.1t). What is the concentration of the substance after 10 minutes?
- A0.50 mol/L
- B0.05 mol/L
- C0.31 mol/L
- D0.18 mol/L
Show answer & explanationAnswer & explanation
Correct answer: D. 0.18 mol/L
To find the concentration after 10 minutes, substitute t = 10 into the function C(t) = 0.5e^(-0.1t). This gives C(10) = 0.5e^(-0.1 * 10) = 0.5e^(-1). Using a calculator, e^(-1) is approximately 0.3678. So, C(10) = 0.5 * 0.3678 = 0.1839, which rounds to 0.18 mol/L.
Why the other options are wrong
- A. This is the initial concentration (at t=0), not the concentration after 10 minutes.
- B. This results from an incorrect calculation, possibly multiplying 0.5 * 0.1.
- C. This results from a calculation error, possibly using e^0.5 or other incorrect exponent.
Evaluating Exponential Functions
Substituting a given value for the independent variable into an exponential function to find the corresponding output.
- Involves a base raised to a variable exponent.
- Requires calculator for 'e' or other non-integer bases.
- Follows order of operations.
Memory trick: Plug and Play: Substitute the time, then calculate the power!