We are solving for the value of t if C(t) = 19. We can rewrite the equation into
[tex]19=5+17e^{-0.038t}[/tex]
Solving for t, we have
[tex]\begin{gathered} 17e^{-0.038t}=19-5 \\ 17e^{-0.038t}=14 \\ e^{-0.038t}=\frac{14}{17} \\ -0.038t=\ln \frac{14}{17} \\ -0.038t=-0.1941 \\ t=\frac{-0.1941}{-0.038} \\ t\approx5.1 \end{gathered}[/tex]
The bottled water will achieve a temperature of 19 degrees C after 5.1 minutes.
Answer: 5.1 min
