Question

Help with Rate of change?

Answer 1

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.


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


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 and Greg's bodies eliminated the medicine?

Henry's body eliminated the antibiotic faster than Greg's body.

Henry's body eliminated the antibiotic at the same rate as Greg's body.

Henry's body eliminated the antibiotic at half of the rate at which Greg's body eliminated the antibiotic.

Henry's body eliminated the antibiotic at one-fourth of the rate at which Greg's body eliminated the antibiotic.

Answer 2

ok i wont

Answer 3

First lets find the rate of change for the first one, since that one is harder to find. Lets make the initial value 282 since f(0) is not given, so we have f(t)=282(x)^t
now after 1 hour f(1)=265.08 so 265.08=282(x)^1, 265.08=282x
x=0.94
that means the function for that one is given by f(t)=282(0.94)^t,
to find the rate of change we subtract that value in parentheses by 1
1-0.94=.06, 6 percent
now in the second one f(t)=200(0.88)^t, it is 0.88, 1-0.88=0.12=12 percent
C is correct

Answer 4

Oh ok Thanx so much!

Answer 5

no problem cam :)