Application of Real Numbers 43. As a cold front moved through the city, the temperature dropped rapidly from \( 75^{\circ} \mathrm{F} \), falling \( \frac{2}{3} \) of a degree each minute. The change in temperature \( t \) minutes after the cold front moved through could be represented by the expression \( -\frac{2}{3} t+75 \). What was the temperature 30 minutes after the cold front moved through?

To find the temperature 30 minutes after the cold front, we can substitute \( t = 30 \) into the expression \( -\frac{2}{3} t + 75 \). Calculating this gives: \[ -\frac{2}{3} \times 30 + 75 = -20 + 75 = 55 \] So, the temperature 30 minutes after the cold front moved through was \( 55^{\circ} \mathrm{F} \). Understanding real numbers in this context is super practical! For instance, temperature changes can affect everything from daily clothing choices to heating costs. Mathematically, real numbers aren't just numbers; they represent quantities that can be rational or irrational, and in this case, they aid in modeling real-world situations like weather changes. If you're interested in diving deeper into the world of real numbers, consider exploring their uses in various fields like physics, engineering, or economics! Books like "Real Analysis" can provide a thorough mathematical background, or even practical ones like "The Joy of x" by Steven Strogatz can illuminate how these concepts impact everyday life.