rajkumarrithvik rajkumarrithvik

20-11-2018
Mathematics

contestada

uppose y left parenthesis t right parenthesis equals 30 e to the power of 4 t end exponent plus 17 represents the number of bacteria present at time t minutes. At what time will the population reach 125 bacteria? (Note: Answers are expressed in terms of the natural logarithm)

Respuesta :

alessandroarenas alessandroarenas

20-11-2018

[tex]y(t) = 30e^{4t} + 17[/tex]

You want

[tex]y(t) = 125[/tex]

Then,

[tex]30e^{4t} + 17 = 125[/tex]

[tex]30e^{4t} = 108\\\\e^{4t} = \frac{54}{15}\\4t = ln\left(\frac{54}{15}\right)[/tex]

Therefore

[tex]t = \frac{1}{4}ln(\frac{54}{15})[/tex] minutes

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