Apatient is given a 100-milligram dosage of a drug that decays exponentially at a rate of 11% per hour. the doctor wants to know when 15 milligrams of the drug remains. write an equation that models the situation. explain each aspect of your equation.

16.3 hours.

Step-by-step explanation:

"Decays exponentially at a rate of 11% per hour" translates into

(1 - 0.11)^h, where h is the number of hours during which the drug decays.

The negative sign comes from "decay."

The complete formula applicable here is

d(h) = (100 mg)(1 - 0.11)^h, where h is the number of hours.  

We want to know how many hours it will be until all but 15 mg remain.  The appropriate formula for this is

15 mg = (100 mg)()^h.  Dividing both sides by 100 mg, we get:

 15 mg

= 0.89^h, or 0.15 = 1.11^h

100 mg

Apply properties of logs to solve this.  Take the natural log of both sides of the above equation.  We get:

ln 0.15 = h(ln 0.89).  Dividing both sides by ln 0.89, we get:

h = 16.3

The original 100 mg dosage would decay to 15 mg after 16.3 hours.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.