Suppose that a medication has a half-life of 5 hours in a patient’s blood stream. if an initial dose of 40.0 mg is administered, how much of the medication will be in the patient’s blood stream after 15 hours? show work or explain your reasoning.

The medication in the patient’s blood stream after 15 hours will be 5mg

Step-by-step explanation:

we can use formula

P(t) is the amount of dose after t hours

t is the time in hours

Po is the initial amount of dose

h s the half life time

we are given

a medication has a half-life of 5 hours in a patient’s blood stream

an initial dose of 40.0 mg is administered

so, we have

now, we can plug these values

now, we can plug t=15

So, the medication in the patient’s blood stream after 15 hours will be 5mg

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}