Question

t hours, C is milligrams per liter: is modeled by formula: C(t)=13(0.74)^t what is initial amount of milligrams per liter and how many hours will it take to decrease by 40% of it's initial level?

Answer 1

\[C(t)=13(0.74)^t\]To find the initial amount, simply calculate the value of \(C(0)\)

To decrease by 40% of its initial level is to decrease to 1-40% = 1-0.4 = 0.6

\[0.6 = \frac{C(t)}{C(0)} = \frac{13(0.74)^t}{13(0.74)^0} = 0.74^t\]Solve for the value of \(t\)

Answer 2

To find the initial quantity, we calculate the value of \(C(0)\):
\[C(0) = 13(0.74)^0 = 13*1 = 13\]

Answer 3

Generally, in these exponential problems, the coefficient of the exponential is the initial amount, and the exponential term = 1 at t = 0.

Answer 4

You might see this written as \[C(t) =C_0(0.74)^t\]where \(C_0 = 13\)

Answer 5

To find the point at which it has decreased by 40%, we can either use the method I suggested earlier, or solve for \(C(t) = C_0 - C_0*40\% = 0.6C_0\)
\[0.6C_0 = C_0(0.74)^t\]\[0.6 = (0.74)^t\]\[\log 0.6 = t\log 0.74\]\[t = \frac{\log 0.6}{\log 0.74} =\]

Answer 6

1.70

Answer 7

Yes. Here's a graph:

Answer 8

The y-axis on that graph represents \(C(t)/C_0\)

Answer 9

ok, so yes it would decrease until it reached zero.

Answer 10

The half life of the substance in this equation is 2.30201 hours.

Answer 11

We could plot \[C(t) = C_0*2^{-t/2.30201}\]on the same graph and the curves would be identical.

Answer 12

I'm studying for a final and I'm trying to put together notes for my study guide. It's so very hard to remember everything mathematically when the problems become so involved. I tend to miss steps occasionally. I appreciate you taking the time to help me work this out correctly.

Answer 13

When's the final?

Answer 14

And what's course? I could try to point you at some select tidbits, possibly.

Answer 15

Tomorrow. Many of the algebraic concepts I can grasp but sometimes I get stuck on little things. I'm not good at being able to think backward. So many of the LOG problems and symbolic interpretations I struggle with.

Answer 16

Ah, i probably won't be able to do much in that case, except to wish you well! Do you have an example of a log problem that trips you up that I could go through quickly before I turn in for the night?

Answer 17

It's a math 111 course. I took all these previous math courses including 211,212 and 213. Then when I switched majors I needed to go back to math 111. As you can tell, I'm somewhat rusty. It's been a few years. lol

Answer 18

Thank you for your help. I should be alright. I've written down many of the inverse properties and such so I'm not flailing about. lol I just figured, I can't ever be too prepared. I only wish I had found this site sooner!

Answer 19

You sound like you're much more prepared than I ever was :-) If you run into some problem that trips you up on the test, I'd be happy to try to work it with you afterwards if you can remember the general outline.

Answer 20

I have to take one more math class after I complete this one. So I'll definitely keep you in mind if I struggle next term at all. Thanks for being patient :) I like this site and the people on it