Multiple choice

A tank contains $40 l $ of solution containing $2 g$ of substance per liter. Salt water containing $3 g$ of this substance per liter runs in at the rate of $4 l/min$ and the well-stirred mixture runs out at the same rate. Find the amount of substance in the tank after $15 minutes$ (in grams).

  1. $110.075$
  2. $121.075$
  3. $111.075$
  4. $211.075$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a differential equation problem: dA/dt = (rate_in * conc_in) - (rate_out * conc_out). dA/dt = (4 * 3) - (4 * A/40) = 12 - A/10. Solving this with A(0) = 80 gives A(t) = 120 - 40e^(-t/10). At t=15, A(15) = 120 - 40e^(-1.5) = 120 - 40(0.2231) = 120 - 8.924 = 111.076.

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