We appreciate your visit to You drink a beverage with 120 milligrams of caffeine Each hour tex h tex the amount of caffeine tex c tex in your system decreases. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Let's solve the problem step-by-step using the given model for caffeine reduction:
1. Understanding the Model: The equation [tex]\( c(h) = 120 \times (0.79)^h \)[/tex] describes how the caffeine level decreases in your system. Here, 120 milligrams is the initial amount, 0.79 represents the remaining percentage after each hour, and [tex]\( h \)[/tex] is the number of hours.
2. Substituting the Values: We need to find [tex]\( c(5) \)[/tex], which involves substituting [tex]\( h = 5 \)[/tex] into the equation:
[tex]\[
c(5) = 120 \times (0.79)^5
\][/tex]
3. Calculating the Caffeine Amount: Now, compute [tex]\( (0.79)^5 \)[/tex] first and then multiply it by 120 to find the remaining caffeine:
[tex]\[
(0.79)^5 = 0.308915776
\][/tex]
[tex]\[
c(5) = 120 \times 0.308915776 = 36.9
\][/tex]
4. Interpreting the Result: After 5 hours, approximately 36.9 milligrams of caffeine will remain in your system.
Therefore, the correct answer is:
b. [tex]\( c(5) = 36.9 \)[/tex]. There will be 36.9 milligrams of caffeine remaining in your system after 5 hours.
1. Understanding the Model: The equation [tex]\( c(h) = 120 \times (0.79)^h \)[/tex] describes how the caffeine level decreases in your system. Here, 120 milligrams is the initial amount, 0.79 represents the remaining percentage after each hour, and [tex]\( h \)[/tex] is the number of hours.
2. Substituting the Values: We need to find [tex]\( c(5) \)[/tex], which involves substituting [tex]\( h = 5 \)[/tex] into the equation:
[tex]\[
c(5) = 120 \times (0.79)^5
\][/tex]
3. Calculating the Caffeine Amount: Now, compute [tex]\( (0.79)^5 \)[/tex] first and then multiply it by 120 to find the remaining caffeine:
[tex]\[
(0.79)^5 = 0.308915776
\][/tex]
[tex]\[
c(5) = 120 \times 0.308915776 = 36.9
\][/tex]
4. Interpreting the Result: After 5 hours, approximately 36.9 milligrams of caffeine will remain in your system.
Therefore, the correct answer is:
b. [tex]\( c(5) = 36.9 \)[/tex]. There will be 36.9 milligrams of caffeine remaining in your system after 5 hours.
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