Question

Sheila is taking medicine to help fight an infection. The function f(x) = 12(0. 82)^x models the amount of a 12-mg dose of antibiotic left in her bloodstream after x hours.
About how many mg are left in her bloodstream after 2 hours?

Answer 1

Given:

$f(x)=12(0.82)^x$

where, f(x) is the amount of a 12-mg dose of antibiotic left in her bloodstream after x hours.

To find:

The remaining mg in her bloodstream after 2 hours.

Solution:

The amount of a 12-mg dose of antibiotic left in her bloodstream after x hours is represented by the function

$f(x)=12(0.82)^x$

Putting x=2, we get the remaining mg in her bloodstream after 2 hours.

$f(2)=12(0.82)^2$

$f(2)=12(0.6724)$

$f(2)=8.0688$

Therefore, the remaining mg in her bloodstream after 2 hours is 8.0688 mg.