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Apply Logarithmic Functions In this activity, you will investigate how logarithmic functions are used to model situations in many different fields. Problem 1: A Caffeine Problem The half-life of caffeine is approximately 5 hours; this means that approximately ½ of the caffeine in the bloodstream is eliminated every 5 hours. Suppose you drink a can of Instant Energy, a 16-ounce energy drink that contains 160 mg of caffeine. Suppose the caffeine in your bloodstream peaks at 160 mg. 1au1 1. How much caffeine will remain in your bloodstream after 5 hours? 10 hours? 1 hour? 2 hours? Record your answers in the table. Explain how you came up with your answers. (You can return to your answers later to make any corrections if you find your strategy was incorrect.) ba4 Time (hours) since 0 peak level reached a Caffeine bloodstream (mg) in 160 1 2 5 10 5720) In..EXPRESS uted proper. 2. Write an exponential function f to model the amount of caffeine remaining in the blood stream t hours after the peak level. What does your exponent need to represent? How can you determine this exponent if you know the number of hours that has passed? eliblede 3. Use the function you wrote in question (2) to check your answers for the table in question (1). Make any necessary corrections. (Be careful when entering fractional exponents in the calculator. Use parentheses.) trigong orth one 4. Determine the amount of caffeine remaining in the bloodstream 3 hours after the peak level. What about 8 hours after peak level? 20 hours? Apply-Logarithmic Functions In this activity, you will investigate how logarithmic functions are used to model situations in many different fields. Problem 1:A Caffeine Problem The half-life of caffeine is approximately 5 hours; this means that approximately / of the caffeine in the bloodstream is eliminated every 5 hours.Suppose you the caffeine in your bloodstream peaks at 160 mg. 1How much caffeine will remain in your bloodstream after 5 hours? 10 hours1 hour 2 hours? Record your answers in the table.Explain how you came up with your answers.You can return to your answers later to make any corrections if you find your strategy was incorrect. Time hourssince 2 10 peak level reached Caffeine in 160 bloodstream(mg 2. Write an exponential function f to model the amount of caffeine remaining in the blood stream t hours afler the peak level. What does your exponent need to represent? How can you determine this exponent if you know the number of hours that has passed? 3.Use the function you wrote in question 2 to check your answers for the table in question (1. Make any necessary corrections.Be careful when entering fractional exponents in the calculator.Use parentheses.) 4. Determine the amount of caffeine remaining in the bloodstream 3 hours after the peak level.What about 8 hours after peak level?20 hours?

Name: apply logarithmic functions in this activity you will investigate how logarithmic functions are used to model situations in many different fields problem 1 a caffeine problem the half life o 21507
Uploaded: 2021-07-26T18:27:53-08:00
Duration: 8 min 26 s
Channel: Carolyn Behr-Jerome
Description: apply logarithmic functions in this activity you will investigate how logarithmic functions are used to model situations in many different fields problem 1 a caffeine problem the half life o 21507

          Apply Logarithmic Functions In this activity, you will investigate how logarithmic functions are used to model situations in many different fields. Problem 1: A Caffeine Problem The half-life of caffeine is approximately 5 hours; this means that approximately ½ of the caffeine in the bloodstream is eliminated every 5 hours. Suppose you drink a can of Instant Energy, a 16-ounce energy drink that contains 160 mg of caffeine. Suppose the caffeine in your bloodstream peaks at 160 mg. 1au1 1. How much caffeine will remain in your bloodstream after 5 hours? 10 hours? 1 hour? 2 hours? Record your answers in the table. Explain how you came up with your answers. (You can return to your answers later to make any corrections if you find your strategy was incorrect.) ba4 Time (hours) since 0 peak level reached a Caffeine bloodstream (mg) in 160 1 2 5 10 5720) In..EXPRESS uted proper. 2. Write an exponential function f to model the amount of caffeine remaining in the blood stream t hours after the peak level. What does your exponent need to represent? How can you determine this exponent if you know the number of hours that has passed? eliblede 3. Use the function you wrote in question (2) to check your answers for the table in question (1). Make any necessary corrections. (Be careful when entering fractional exponents in the calculator. Use parentheses.) trigong orth one 4. Determine the amount of caffeine remaining in the bloodstream 3 hours after the peak level. What about 8 hours after peak level? 20 hours?
Apply-Logarithmic Functions In this activity, you will investigate how logarithmic functions are used to model situations in many different fields. Problem 1:A Caffeine Problem The half-life of caffeine is approximately 5 hours; this means that approximately / of the caffeine in the bloodstream is eliminated every 5 hours.Suppose you the caffeine in your bloodstream peaks at 160 mg. 1How much caffeine will remain in your bloodstream after 5 hours? 10 hours1 hour 2 hours? Record your answers in the table.Explain how you came up with your answers.You can return to your answers later to make any corrections if you find your strategy was incorrect. Time hourssince 2 10 peak level reached Caffeine in 160 bloodstream(mg
2. Write an exponential function f to model the amount of caffeine remaining in the blood stream t hours afler the peak level. What does your exponent need to represent? How can you determine this exponent if you know the number of hours that has passed?
3.Use the function you wrote in question 2 to check your answers for the table in question (1. Make any necessary corrections.Be careful when entering fractional exponents in the calculator.Use parentheses.)
4. Determine the amount of caffeine remaining in the bloodstream 3 hours after the peak level.What about 8 hours after peak level?20 hours?

apply logarithmic functions in this activity you will investigate how logarithmic functions are used to model situations in many different fields problem 1 a caffeine problem the half life o 21507

Added by Cynthia S.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Carolyn Behr-Jerome

07/26/2021

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Step 1: The half-life of caffeine is approximately 5 hours, which means that approximately 1/2 of the caffeine in the bloodstream is eliminated every 5 hours. Show more…

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Apply Logarithmic Functions In this activity, you will investigate how logarithmic functions are used to model situations in many different fields. Problem 1: A Caffeine Problem The half-life of caffeine is approximately 5 hours; this means that approximately ½ of the caffeine in the bloodstream is eliminated every 5 hours. Suppose you drink a can of Instant Energy, a 16-ounce energy drink that contains 160 mg of caffeine. Suppose the caffeine in your bloodstream peaks at 160 mg. 1au1 1. How much caffeine will remain in your bloodstream after 5 hours? 10 hours? 1 hour? 2 hours? Record your answers in the table. Explain how you came up with your answers. (You can return to your answers later to make any corrections if you find your strategy was incorrect.) ba4 Time (hours) since 0 peak level reached a Caffeine bloodstream (mg) in 160 1 2 5 10 5720) In..EXPRESS uted proper. 2. Write an exponential function f to model the amount of caffeine remaining in the blood stream t hours after the peak level. What does your exponent need to represent? How can you determine this exponent if you know the number of hours that has passed? eliblede 3. Use the function you wrote in question (2) to check your answers for the table in question (1). Make any necessary corrections. (Be careful when entering fractional exponents in the calculator. Use parentheses.) trigong orth one 4. Determine the amount of caffeine remaining in the bloodstream 3 hours after the peak level. What about 8 hours after peak level? 20 hours? Apply-Logarithmic Functions In this activity, you will investigate how logarithmic functions are used to model situations in many different fields. Problem 1:A Caffeine Problem The half-life of caffeine is approximately 5 hours; this means that approximately / of the caffeine in the bloodstream is eliminated every 5 hours.Suppose you the caffeine in your bloodstream peaks at 160 mg. 1How much caffeine will remain in your bloodstream after 5 hours? 10 hours1 hour 2 hours? Record your answers in the table.Explain how you came up with your answers.You can return to your answers later to make any corrections if you find your strategy was incorrect. Time hourssince 2 10 peak level reached Caffeine in 160 bloodstream(mg 2. Write an exponential function f to model the amount of caffeine remaining in the blood stream t hours afler the peak level. What does your exponent need to represent? How can you determine this exponent if you know the number of hours that has passed? 3.Use the function you wrote in question 2 to check your answers for the table in question (1. Make any necessary corrections.Be careful when entering fractional exponents in the calculator.Use parentheses.) 4. Determine the amount of caffeine remaining in the bloodstream 3 hours after the peak level.What about 8 hours after peak level?20 hours?

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00:01 In this video, we're going to look at logarithmic transformations and the power law model.

00:06 We can use a logarithmic transformation to determine if the power law is a good, the power law model is actually a good fit for our data.

00:15 Now, the power law formula is right here.

00:20 Y equals alpha -x to the beta.

00:23 And in our particular example, x represents the time in microseconds, and y equals the amps built up.

00:32 The circuit at time x.

00:35 So here are x's and here's our y.

00:37 First thing we're asked to do is we're asked to find x prime and y prime.

00:41 These are our transformations.

00:42 So x prime will be log of x and y prime will be log of y.

00:46 And then we're asked to graph.

00:51 Actually we're asked to find the regression model for the graph of x prime y prime.

01:05 So i would find log of 2.

01:07 This would be my first x and then i'm going around it so log of two again on the calculator log two and then i would also need to find log 1 .81 and i can do that for each of my values and then i would graph that information but there's actually a faster way to do it so i'll go back to my calculator but this time i'm going to go to my lists so stat number one edit and notice i already have the information in l1 and l2.

01:58 What i'm going to do on l3 and l4 is figure out the logs of those values.

02:04 So i'm going to type log 2, so log of my original x value, and press enter, and you can see this automatically calculates it for me.

02:14 So i don't have to go through and do it all by hand.

02:18 Log 4, log 6, log 8, log 10.

02:26 And remember the log of 10 is 1 because those are inverses.

02:30 All right, i'm going to pause the video and then i'm going to enter in the logs of the y values.

02:37 And when i come back or in a second, you will see the results of that.

02:44 So now i have the log of my y, each y value entered into l4.

02:49 So to find the regression model, select stat, cursor over to calc, choose number 8, the linear regression model in the form of a plus bx.

02:57 But i don't want l1, l2, i want l3 and l4.

03:01 So second three will put l3 under my x list.

03:05 Second four puts l4 under my y list, cursor down to calculate.