Question

Henry is taking a medicine for a common cold. His body metabolizes the medicine over a certain time interval. The table below shows the amount of medicine f(t), in mg, that was present in Henry's body after time t:

Answer 1

t (hours) 1 2 3 4 5
f(t) (mg) 282 265.08 249.18 234.22 220.17

Answer 2

Greg was administered 200 mg of the same medicine. The amount of medicine in his body f(t) after time t is shown by the equation below:

\[f(t)=200(0.88)^{t}\]

Which statement best describes the rate at which Henry’s and Greg's bodies eliminated the medicine?

Answer 3

Which statement best describes the rate at which Henry’s and Greg's bodies eliminated the medicine?

Answer 4

(A) Henry's body eliminated the antibiotic faster than Greg's body.
(B) Henry's body eliminated the antibiotic at the same rate as Greg's body.
(C) Henry's body eliminated the antibiotic at half of the rate at which Greg's body eliminated the antibiotic.
(D) Henry's body eliminated the antibiotic at one-fourth of the rate at which Greg's body eliminated the antibiotic.

Answer 5

@TheSmartOne @hartnn @iambatman @paki I need help with this question plz

Answer 6

@hartnn any idea about this question please...?

Answer 7

@iGreen @sammixboo @mathmath333 @Michele_Laino I really need help on this question guys. Please help me out.

Answer 8

I'm trying...

Answer 9

Thank you!

Answer 10

data referring to Greg, are:
1--->176
2--->154.88
3--->136.3
4--->120
5--->105.5

Answer 11

okay I understand that

Answer 12

I used the formula above

Answer 13

\[176=200(0.88)^{1}\]

Answer 14

that's right!

Answer 15

And so on by changing the exponent until 5

Answer 16

yes!

Answer 17

I understand those parts but I just don't know what to do next

Answer 18

now, we can try to find the percentage reduction of the antibiotic in both Greg and Henry bodies.
So in the case of Greg, we have to solve this equation
\[176-\frac{ p }{ 100 }*176=105.5\]

Answer 19

p is the percentage rate of elimination of the antibiotic from Greg

Answer 20

okay. what's next?

Answer 21

we have to solve that equation for p, namely we have to find the value of p

Answer 22

how do we do that?

Answer 23

first I subtract from both sides 105.5, namely:
\[176-\left( \frac{ p }{ 100 }*176 \right)-105.5=105.5-105.5\]

Answer 24

so, we have:
\[70.5-\left( \frac{ p }{ 100 }*176 \right)=0\]

Answer 25

then:
\[70.5=\frac{ p }{ 100 }*176\]

Answer 26

finally:
\[p=\frac{ 70.5 }{ 176 }*100=40\]

Answer 27

so Greg body eliminates the antibiotic at a rate of about 40%

Answer 28

okay I get that

Answer 29

Now, we have to solve the same equation for Henry, using the data referring to Henry.
So we have to solve this equation:
\[282-\frac{ q }{ 100 }*282=220.17\]

Answer 30

like before, I subtract from both sides 220.17:
\[282-\left( \frac{ q }{ 100 }*282 \right)-220.17=220.17-220.17\]

Answer 31

so:
\[61.83-\left( \frac{ q }{ 100 }*282 \right)=0\]

Answer 32

then:
\[\frac{ q }{ 100 }*282=61.83\]

Answer 33

finally:
\[q=\frac{ 61.83*100 }{ 282 }=22\]

Answer 34

so its the third option?

Answer 35

so we can say that Henry body eliminates the antibiotic at a rate of about 22%, namely about the half of the rate of Greg

Answer 36

bcuz 22/40 is equal to 0.55 which is closer to 0.5

Answer 37

yes!

Answer 38

Thank YOU SO MUCHH! You were very helpful.

Answer 39

Thank you!