The amount of caffeine in the bloodstream decreases by 26% every hour.A cup of coffee contains 94 mg of caffeine. Define a function, fthat gives the amount of caffeine remaining in the blood stream thours after the coffee was consumed. How many hours will it take for the amount of caffeine to reach half of the amount in the initial cup of coffee?hours A double shot of espresso contains 126 mg of caffeine. Define a function, g, that gives the amount of caffeine remaining in the blood stream x hours after the espresso was consumed. How many hours will it take for the amount of caffeine to reach half of the amount in the initial espresso?hoursA can of Rock Star energy drink has 180 mg of caffeine in it. How long after you consume the Rock Star will the caffeine in your blood stream decrease to 90 mg?hoursTrue or False: The number of hours it takes for the amount of caffeine in your body to reach half of the amount initially in your body depends on the initial amount of caffeine in your body.

Question
Asked Nov 2, 2019
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The amount of caffeine in the bloodstream decreases by 26% every hour.

  1. A cup of coffee contains 94 mg of caffeine. Define a function, f

that gives the amount of caffeine remaining in the blood stream t

hours after the coffee was consumed.

 

  • How many hours will it take for the amount of caffeine to reach half of the amount in the initial cup of coffee?

    hours

  • A double shot of espresso contains 126 mg of caffeine. Define a function, g

, that gives the amount of caffeine remaining in the blood stream x

 

hours after the espresso was consumed.

 

  • How many hours will it take for the amount of caffeine to reach half of the amount in the initial espresso?

    hours

  • A can of Rock Star energy drink has 180 mg of caffeine in it. How long after you consume the Rock Star will the caffeine in your blood stream decrease to 90 mg?

    hours

  • True or False: The number of hours it takes for the amount of caffeine in your body to reach half of the amount initially in your body depends on the initial amount of caffeine in your body.

 

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Expert Answer

Step 1

Hi, your question has six sub questions. We answer upto three sub questions as per our policy. Please repost the next three as a separate question.

Step 2

Formula for exponential decay is given as,

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xa(1-r where. x Final Value a Initial Value r =rate of change t = time period In the question given. r 26% a93mg tthours Therefore the expression is written as 26 93| 1- 100 x 93(0.74) We write the function fas a function of variable t as, f()93 (0.74)

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Step 3

To determine t, w...

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26 93 = 93 1 2 100 93 93 1 2 26 100 26 2 100 Taking log on both sides 26 = tln 1- 100 In 74 = tln 100 n -0.6931 =(0.3011) t 2.3020 hours

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Tagged in

Math

Calculus

Functions