Question

If a hospital patient is given 50 milligrams of medicine which leaves the bloodstream at 10% per hour, how many milligrams of medicine will remain in the system after 6 hours? Use the function A(t) = Iert. (1 point)


12.39 mg
27.44 mg
45.24 mg
91.11 mg

Answer 1

\[\Large\rm A(\color{orangered}{t})=\mathcal I e^{r\color{orangered}{t}}\]Ok, so I represents the `initial amount`.
Looks like the patient was given 50 to start, yes? :)\[\Large\rm A(\color{orangered}{t})=50 e^{r\color{orangered}{t}}\]

Answer 2

Ok, now what?

Answer 3

Mmm let's make sure we're understanding what the rate, \(\Large\rm r\), should be.
Hmm

Answer 4

If 10% is leaving the bloodstream each hour,
then 90% will remain, yah?

Answer 5

Ok, yes.

Answer 6

Remember how to write 90% as a decimal?
We want it as a decimal when we toss it into the equation.

Answer 7

0.9

Answer 8

\[\Large\rm A(\color{orangered}{t})=50 e^{0.9\cdot\color{orangered}{t}}\]Ok good.

Answer 9

So t represents time, more specifically, hours.
So they want us to calculate the amount of medicine in the patients system at time t=6 hours.

Answer 10

\[\Large\rm A(\color{orangered}{6})=50 e^{0.9\cdot\color{orangered}{6}}\]

Answer 11

And then we let the calculator do the work from there :)

Answer 12

Ooo that did not give a nice calculator answer :3 sec lemme check that again..

Answer 13

Mmm I guess I screwed up the rate :(
Or the question was worded poorly, one of those two things lol. I'm not sure >.<
So we were supposed to use the 10%, not the 90%.\[\Large\rm A(\color{orangered}{6})=50 e^{0.1\cdot\color{orangered}{6}}\]

Answer 14

Do you have a calculator?

Answer 15

Yeah, I can use mathway.com , but I don't know how to input it. Can you do it?

Answer 16

Put it into the calculator something like this,\[\Large 50\times e\text{^}(0.1\times6)\]

Answer 17

I can't input that for some reason :(

Answer 18

In mathway it should look like this:\[\Large\rm 50\cdot e^{(0.1\cdot6)}\]

Answer 19

No why not? D:

Answer 20

ok so I got 91.10

Answer 21

Ok good! :)
Make sure you round to the hundredth place correctly though.
That's a 5 as the next number ya?

Answer 22

91.105

Answer 23

right, so 91.11 :)

Answer 24

I got it wrong!

Answer 25

Was not D? D:

Answer 26

No it wasn't D...that's so weird!

Answer 27

Wait wait why would it be D, if he started with 50 milligrams and its decreasing,
how does he end up with 90 later on.

omggggg im stupid today >.<

Answer 28

*cri*

Answer 29

Omg so what is it?

Answer 30

\[\Large\rm A(\color{orangered}{6})=50 e^{(-0.1\cdot\color{orangered}{6})}\]Negative 10%, 10 percent leaving the bloodstream.
Which works out to 27.440581 mg.

I think that's the right answer.
Ahhh I'll have to brush up on my exponential decay problems :( ugh

Answer 31

oh ok. Thank you