Question

Maureen is taking an antibiotic. Her body metabolizes the antibiotic over a certain time interval. The table below shows the amount of antibiotic f(t), in mg, that was present in her body after time t:

t (hours) 1 2 3 4 5
f(t) (mg) 150 90 54 32.4 19.4


Ken was administered 200 mg of the same antibiotic. The amount of antibiotic f(t) in his body after time t is shown by the equation below:
f(t) = 200(0.976)t

Answer 1

Which statement best describes the rate at which Maureen’s and Ken's bodies eliminated the antibiotic between 1 hour to 4 hours?

Maureen's body eliminated the antibiotic faster than Ken's body.

Maureen's body eliminated the antibiotic at the same rate as Ken's body.

Maureen's body eliminated the antibiotic at half of the rate at which Ken's body eliminated the antibiotic.

Maureen's body eliminated the antibiotic at one-fourth of the rate at which Ken's body eliminated the antibiotic.

Answer 2

@ganeshie8 @jdoe0001 @dan815 @aaronq @Venny

Answer 3

Is the t supposed to be an exponent, like \(\sf f(t) = 200(0.976)^t\) ?

Answer 4

yes

Answer 5

i think so.

Answer 6

Okay, so what the question asks is to compare the rates of clearance.

Find the concentrations for Ken at t=1, 2, 3, 4 to compare them with Maureen's.

Answer 7

really not understnding

Answer 8

Find the amounts left at t=1, 2, 3, 4

Ken: \(\sf f(t)=200(0.976)^t\)

\(\sf f(1)=195.2 ~mg\)
\(\sf f(2)=190.5~mg\)

etc

Answer 9

is this what i compare

Answer 10

You compare Ken's data (above) with Maureen's data (given in the question).

Answer 11

its the same.

Answer 12

Maureen's body eliminated the antibiotic at the same rate as Ken's body.

Answer 13

thats not what it seems like to me

Maureen from t=1 to t=2, went from 150 to 90

a loss of 40 mg in 1 hour

Ken lost ~5mg in that same first hour

Answer 14

so kens body eliminated it faster? how?

Answer 15

What did you multiply?

Answer 16

not ken maureen.

Answer 17

yeah, look at the rates between the same time intervals

Answer 18

Maureens body eliminated it faster.

Answer 19

indeed!

Answer 20

A

Answer 21

can you help with 1 more

Answer 22

sure thing!

Answer 23

The functions f(x) and g(x) in the table below show Jane’s and Mariah's savings respectively, in dollars, after x days. Some values are missing in the table:

x(years) 1 2 3

f(x) = 2x
Jane’s savings in dollars
2 4

g(x) = 2x
Mariah’s savings in dollars
2 4


Which statement best describes Jane and Mariah's savings in the long run?

Jane will save more than Mariah.

Mariah will save more than Jane.

The savings will increase by the same factor for both.

The savings will increase by the same percentage for both.

Answer 24

I chose B

Answer 25

Are both of the functions \(2x\) or \(2^x\)?

Answer 26

its 2x and 2^x

Answer 27

they are both different

Answer 28

You can see that \(2x\) is linear and will increase at a constant rate, but \(2^x\) is exponential and will increase MUCH faster

Answer 29

so B.

Answer 30

Mariah will save more than Jane.

Answer 31

since its going up does that mean there's a loss in the money she has?

Answer 32

nope, the graphs are their savings, no money is being lost here.

The one with the exponential function will save more, but i dont know which on of the persons has it because they look the same to me

Answer 33

what do you mean the same?

Answer 34

The percentage?

Answer 35

i mean from what you pasted, both of the functions look like "2x" so i dont know which one of the girls in the question has the exponential function.

Answer 36

f(x) = 2x
Jane’s savings in dollars

Answer 37

g(x) = 2^x
Mariah’s savings in dollars

Answer 38

sorry i confused you

Answer 39

no worries! so yeah you were right, Mariah will save more, so B would be right

Answer 40

Thank so much :)

Answer 41

no problem :)