Question

If a hospital patient is given 100 milligrams of medicine, which leaves the bloodstream at 14% per hour, how many milligrams of medicine will remain in the system after 10 hours? Use the function A(t) = Iert. 24.66 mg 86.94 mg 90.48 mg 405.52 mg

Answer 1

Answer:

24.66 mg of medicine will be left.

Step-by-step explanation:

The given exponential equation is,

$A(t)=ie^{rt}$

Where,

A(t) = amount after time t

i = initial amount = 100 mg

r = rate of change = -14% = -0.14 (-ve is taken because the amount is decreasing)

t = time = 10 hours

Putting the values,

$A(t)=100e^{-0.14\times 10}$

$=100e^{-1.4}$

$=24.66\ mg$

Answer 2

The medication is an illustration of an exponential function.

The number of milligrams left after 10 hours is 24.66 mg

The given parameters are:

$\mathbf{I = 100}$ --- initial milligrams

$\mathbf{r = -0.14}$ --- the rate per hour (it is negative, because it reduces the content of the medicine)

$\mathbf{t = 10}$ --- time

The function is given as:

$\mathbf{A(t) = Ie^{rt}}$

So, we have:

$\mathbf{A(10) = 100 \times e^{-0.14 \times 10}}$

$\mathbf{A(10) = 100 \times e^{-1.4}}$

$\mathbf{A(10) = 100 \times 0.2466}$

$\mathbf{A(10) = 24.66}$

Hence, the number of milligrams left after 10 hours is 24.66 mg

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