Isolating t, we have that:
a) We would have the inverse function, which would given the number of hours until there are N bacteria.
b) [tex]t = -\ln{\left(\frac{5000}{N(t)}\right)[/tex]
The number of bacterial cells after t hours in their sample once the medicine is introduced is modeled by the equation:
[tex]N(t) = 5000e^{-t}[/tex]
Item a:
Isolating t, we would have the inverse function, which would given the number of hours until there are N bacteria.
Item b:
[tex]N(t) = 5000e^{-t}[/tex]
[tex]e^{-t} = \frac{5000}{N(t)}[/tex]
[tex]\ln{e^{-t}} = \ln{\left(\frac{5000}{N(t)}\right)[/tex]
[tex]-t = \ln{\left(\frac{5000}{N(t)}\right)[/tex]
[tex]t = -\ln{\left(\frac{5000}{N(t)}\right)[/tex]
You can learn more about inverse logarithmic functions at https://brainly.com/question/26499627
