BertramW119466 BertramW119466
  • 25-10-2022
  • Mathematics
contestada

Finding the time given an exponential function with base e that models a real-world situation

Finding the time given an exponential function with base e that models a realworld situation class=

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CosetteV177523 CosetteV177523
  • 25-10-2022

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

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