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.