When you drink a cup of coffee or a glass of cola, or when you eat a chocolate bar, the percent, P, of caffeine remaining in your bloodstream is related to the elapsed time, t, in hours, by t=5(logP/log0.5).
a) how long will it take for the amount of caffeine to drop to 20% of the amount consumed?
My answer (which is correct)
= 11.6
b) suppose you drink a cup of coffee at 9 am. What percent of the caffeine will remain in your body at noon?
My attempt:
9=5(logP/log0.5)
then I solved for P, but the answer is wrong.
Could you please help me with part b?
Your value for t should be 3, not 9
from 9:00 am to noon is 3 hours.
How do you sovle for P
pls tell me how to solve for p
To find the percent of caffeine remaining in your body at noon, we need to calculate the value of P using the given equation:
t = 5(logP/log0.5)
We know that the time at which we need to find P is 3 hours after 9 am, which is noon. So, we substitute t = 3 into the equation:
3 = 5(logP/log0.5)
To solve this equation for P, we need to isolate the logP term. Let's go through the steps:
Divide both sides by 5:
3/5 = logP/log0.5
Now, multiply both sides by log0.5:
(3/5) * log0.5 = logP
We can use the logarithmic properties to rewrite log0.5 as ln0.5 divided by ln10:
(3/5) * (ln0.5 / ln10) = logP
Now, simplify the expression on the right-hand side:
(3/5) * (-0.301 / 2.303) = logP
Calculate the numerical value:
-0.1818 ≈ logP
To find P, we need to take the antilogarithm of both sides. Since the base of the logarithm is not mentioned, we assume it to be 10 (common logarithm):
P ≈ 10^(-0.1818)
Using a calculator, we find P ≈ 0.651.
So, approximately 65.1% of the caffeine will remain in your body at noon.