Hi there!
[tex]\large\boxed{t = 12.60 \text{ days}}[/tex]
We can solve this by setting the equation equal to 150:
[tex]150 = \frac{230}{1 + 56.5e^-0.37t}[/tex]
Cross-multiply and divide:
[tex]150 (1 + 56.5e^{-0.37t})= 230[/tex]
Divide both sides by 150:
[tex]1 + 56.5e^{-0.37t} = 1.5333[/tex]
Isolate for t by subtracting both sides by 1 and dividing by 56.5:
[tex]56.5e^{-0.37t} = 0.5333[/tex]
[tex]e^{-0.37t} = 0.0094395[/tex]
Take the natural log to solve for t:
[tex]ln (0.0094395) = -0.37t[/tex]
[tex]-4.6628522 = -0.37t[/tex]
Divide both sides by -0.37:
t = 12.60 days.
