A is the amount of caffeine left in your body after two hours, C is the amount of caffeine originally ingested, and k is the half-life of caffeine (about 5.7 hours). Round all other numbers to the thousandths place.
Formula A=C (0.5)2/k
c=29 and k = 5.7
I don't understand how to work this problem can someone show me baby step by baby step or explain like you would a 5 year old.
So you are evaluating
A = c (.5)^(2/5.7)
2/5.7 = appr .350877
so we need (.5)^.350877
If you have a good calculator look for a key function
labeled yx, which we usually type as y^x
enter the base .5
push that yx button
enter .350877
press the = button to get
.7841..
multiply that by 29 for a final answer of
A = 22.739
It's just a matter of button-pushing
Sure! I can explain it step by step for you.
Step 1: Plug in the values given.
You are given that C (the amount of caffeine originally ingested) is 29 and k (the half-life of caffeine) is 5.7. Start by substituting these values into the formula.
A = C * (0.5)^(2/k)
Step 2: Calculate the exponent.
In this step, we need to calculate the value of 2/k.
2/k = 2/5.7 ≈ 0.35088
Step 3: Calculate (0.5)^(2/k).
Now, we need to calculate the value of (0.5)^(2/k).
(0.5)^(2/k) = (0.5)^0.35088 ≈ 0.793
Step 4: Multiply C by the result from Step 3.
Now you need to multiply the value of C (which is 29) by the result you obtained in Step 3 (which is 0.793).
A = 29 * 0.793 ≈ 23.027
Step 5: Round the result.
Lastly, you are asked to round all other numbers to the thousandths place. So, round the result from Step 4 to the nearest thousandths.
A ≈ 23.027 (rounded to the thousandths place)
Therefore, A, the amount of caffeine left in your body after two hours, would be approximately 23.027 (rounded to the thousandths place).
Sure, I would be happy to help you step by step and explain it in a simple way. Let's break down the problem:
First, you are given a formula to calculate the amount of caffeine left in your body after two hours, based on the amount of caffeine originally ingested and the half-life of caffeine.
The formula is: A = C * (0.5)^(2/k)
Now, let's substitute the given values into the formula. You are told that C (the amount of caffeine originally ingested) is 29, and k (the half-life of caffeine) is 5.7.
Step 1: Substitute the values into the formula:
A = 29 * (0.5)^(2/5.7)
Step 2: Calculate the exponent:
2/5.7 ≈ 0.350877
Step 3: Calculate the value inside the parentheses:
(0.5)^0.350877 ≈ 0.781
Step 4: Multiply the result by C:
A ≈ 29 * 0.781
Step 5: Calculate the final result:
A ≈ 22.609
So, after two hours, the approximate amount of caffeine left in your body would be 22.609.
Remember to round the answer to the thousandths place, so the final answer is 22.609.
I hope this step-by-step explanation helps you understand how to work through this problem!