Equation:
t=5(logP/log0.5)
P is the percentage of caffiene in the bloodstream related to t, time elapsed in hours
Suppose you drink a cup of coffee at 9:00 a.m. What percentage of the caffiene will remain in your body at noon?
well, just plug in t=3
To determine the percentage of caffeine remaining in your body at noon, we can substitute the value of t = 3 hours (since 3 hours have elapsed from 9:00 a.m. to noon) into the equation:
t = 5(logP/log0.5)
3 = 5(logP/log0.5)
Now, we need to solve this equation for P.
Divide both sides of the equation by 5:
3/5 = logP/log0.5
Next, we can rewrite the equation using exponential form:
0.5^(3/5) = P
Calculating this value on a calculator, we find:
0.5^(3/5) ≈ 0.6867
Therefore, the percentage of caffeine remaining in your body at noon is approximately 68.67%.
To find out what percentage of the caffeine will remain in your body at noon, we can use the given equation where t represents the time elapsed in hours and P represents the percentage of caffeine in the bloodstream.
First, we need to determine the value of t at noon. Since you drank the coffee at 9:00 a.m. and noon is three hours after that, t = 3.
Now we can substitute the value of t into the equation:
t = 5(log P / log 0.5)
3 = 5(log P / log 0.5)
Next, we can rearrange the equation to isolate P:
(log P / log 0.5) = 3 / 5
Taking both sides of the equation to the power of 0.5:
P = 0.5^(3/5)
Using a calculator to evaluate the right side of the equation:
P ≈ 0.6759
The result, P ≈ 0.6759, represents the percentage of caffeine that will remain in your body at noon. Multiplying this value by 100 to express it as a percentage:
P ≈ 67.59%
Therefore, approximately 67.59% of the caffeine will remain in your body at noon.