4. Tourists from the USA, when traveling to Europe, often use an approximate formula to convert temperatures in degrees Celsius $C$ to the familiar degrees Fahrenheit $F$: $F=2 C+30$. Indicate the range of temperatures (in degrees Celsius) for which the deviation of the temperature in degrees Fahrenheit, obtained using the approximate formula, from the temperature obtained using the exact formula does not exceed $5 \%$. To obtain the exact formula, it should be known that water freezes at $32 F$, and boils at $212 F$.
Answer: $1 \frac{11}{29} \leq C \leq 32 \frac{8}{11}$. Solution. Both temperature scales are uniform, so they are related by a linear law: $F=k C+b$. The constants $a$ and $b$ are determined from the condition. The exact formula is obtained: $F=\frac{9}{5} C+32$.

The deviation of temperatures calculated by the two formulas is: $\frac{(2 C+30)-\left(\frac{9}{5} C+32\right)}{\frac{9}{5} C+32}$ $=\frac{C-10}{9 C+160}$. According to the condition: $-\frac{5}{100} \leq \frac{C-10}{9 C+160} \leq \frac{5}{100}$. From this: $\frac{40}{29} \leq C \leq \frac{360}{11}$. This means that in the temperature range of approximately 1 to 33 degrees Celsius, using the approximate formula is quite justified (since converting degrees using it is much more convenient than using the exact formula).