Question

The number of milligrams of a drug that remains in a patient’s system after t hours is given by the function A(t) = Ie^rt. Juan was given 500 milligrams of medicine which leaves his bloodstream at a rate of 20%. How much of the medicine remains in his system after 6 hours

Answer 1

"Juan was given 500 milligrams" which means the initial amount I is I = 500, so

A(t) = Ie^rt

becomes

A(t) = 500e^rt

Answer 2

i got 111.58 mg

Answer 3

Now in 1 hour, 20% of 500 mg leaves, so you're left with 80% of 500 or 0.8*500 = 400 mg

This means

A(t) = 500e^rt

becomes


400 = 500e^(r*1)

What do you get when you solve for r?

Answer 4

111.58 mg is a bit short of what I'm getting

Answer 5

is 133.90mg closeR?

Answer 6

yes it is, but still not what I'm getting

Answer 7

what did you get for r?

Answer 8

the answer is 150.60 mg! :)

Answer 9

is that what the book says?

Answer 10

there is no book.

Answer 11

oh so that's the computer says?

Answer 12

that's what*

Answer 13

thats the highest choice.

Answer 14

is 131.07 a choice?

Answer 15

133.90 is the closet to that number

Answer 16

hmm maybe something is missing because 131.071 is what I'm getting

Answer 17

im not sure i just checked the problem

Answer 18

Is 104.86 a choice?

Answer 19

the choices are 150.60 mg 133.0mg, 111.58mg,99.20mg

Answer 20

yeah something has to be missing, I'm not getting any of those

Answer 21

no thats the problem. perfectly

Answer 22

This is exponential decay. The equation should be\[A(t)=Ie ^{-rt}\]
Put r = 0.2 and the answer is 150.6mg

Answer 23

You mean r = -0.2, I guess it's that simple...

Answer 24

@jim_thompson5910 The exponent is -rt. You could give the fractional rate a negative sign and say the original equation was correct I guess. :)

Answer 25

oh, in this case, they say that the exponent is just rt...hmm this problem is just off