Rate Of Change

[atcalc]

percentage of toxin in blood t hours after consumption C(t)=.12te^-1/2


Q.
1. at what rate is the toxin/blood level changing at time t?
2. How much time passes before the toxin level begins to decrease?
3. If the toxin limit is 0.04%, how much time can pass before it reaches this level? At what rate is the toxin level decreasing when is reaches this limit?

 

[stapel]

1) To find the rate of change, differentiate.

2) To find the local max, apply the method(s) and Test(s) you've been taught for finding critical points and then categorizing them as maximums or minimums.

3) Plug the given percentage into the given formula, and solve for the specified variable. Plug this value into the derivative to find the rate of change at that point.

If you get stuck, please reply showing all of your work and reasoning so far. Thank you! :wink:

 

[Bahrom7893]

1) Just like Stapel said, to find the rate of change, differentiate (with respect to time). I assumed, that you meant

C(t)=.12t * (e)^(-1/2). I rewrote it like C(t) = [ .12 / { e ^ (1 / 2) } ] * t , then

dC/dt = .12 / { e ^ (1 / 2) }. This is the rate of change of toxin in blood at time t, because e is a constant.

 

[BigGlenntheHeavy]

Q.
1. at what rate is the toxin/blood level changing at time t?
2. How much time passes before the toxin level begins to decrease?
3. If the toxin limit is 0.04%, how much time can pass before it reaches this level? At what rate is the toxin level decreasing when is reaches this limit?

\(\displaystyle C(t) \ = \ \frac{.12}{e^{.5}}t, \ a \ linear \ equation \ with \ constant \ slope \ .072783679166\)

\(\displaystyle 1) \ \frac{dC}{dt} \ = \ \frac{.12}{e^{.5}}\)

\(\displaystyle 2) \ Toxin \ level \ never \ decreases, \ but \ constantly \ increases\)

\(\displaystyle 3) \ This \ toxin \ is \ bad \ news.\)

\(\displaystyle Obviously, \ you \ have \ miswritten \ what \ C(t) \ is.\)