Question

A laboratory is working on medicine for a bacterial infection. The number of bacterial cells in their sample once the medicine is introduced is modeled by the equation N = 5000(e^-t) where N is the number of bacteria cells remaining and t is the number of days.a. The lab decides that they should rewrite their equation to isolate t. What will the new equation tell them?b. Rewrite this equation to isolate t.

Answer 1

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) $t = -\ln{\left(\frac{5000}{N(t)}\right)$

What is the mathematical model?

The number of bacterial cells after t hours in their sample once the medicine is introduced is modeled by the equation:

$N(t) = 5000e^{-t}$

Item a:

Isolating t, we would have the inverse function, which would given the number of hours until there are N bacteria.

Item b:

$N(t) = 5000e^{-t}$

$e^{-t} = \frac{5000}{N(t)}$

$\ln{e^{-t}} = \ln{\left(\frac{5000}{N(t)}\right)$

$-t = \ln{\left(\frac{5000}{N(t)}\right)$

$t = -\ln{\left(\frac{5000}{N(t)}\right)$

You can learn more about inverse logarithmic functions at brainly.com/question/26499627