UNIT 3 SUMMARY STATIONS THROUGHOUT THE NEXT 2 DAYS, WE WILL BE SUMMARIZING THE CONCEPT OF EXPONENTIAL FUNCTIONS AND THEIR VARIOUS APPLICATIONS.

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1 Name: Group Members: UNIT 3 SUMMARY STATIONS THROUGHOUT THE NEXT DAYS, WE WILL BE SUMMARIZING THE CONCEPT OF EXPONENTIAL FUNCTIONS AND THEIR VARIOUS APPLICATIONS. EACH ACTIVITY HAS A COLOR THAT CORRESPONDS TO THE COLOR SHEET FOR THAT ACTIVITY. o PINK GROWTH/ DECAY (VIDEO) o YELLOW POSTER (APPLICATIONS OF EXPONENTIAL FUNCTIONS) o BLUE FAST CARS (DEPRECIATION) o GREEN US POPULATION GROWTH (HISTORY) EACH PERSON IS RESPONSIBLE FOR COMPLETING HIS/ HER OWN ACTIVITY PACKET, HOWEVER COLLABORATION IS EXPECTED. YOUR GRADE WILL BE BASED ON THE WORK YOU SUBMIT AS WELL AS A TEAMWORK GRADE FROM THE RUBRIC THAT CAN BE FOUND ON THE BACK OF THIS SHEET. EACH PERSON IN YOUR GROUP SHOULD INITIAL THE ACTIVITY SHEET AFTER IT IS COMPLETED. IT IS UNDERSTOOD THAT BY ALLOWING YOUR TEAMMATES TO SIGN YOUR SHEET, YOU AGREE THAT HE/ SHE HAS EQUALLY CONTRIBUTED TO THE COMPLETION OF THE ACTIVITY.

2 Math Groupwork Team Assessmet Form Names Block Date Group Assigmet Check the appropriate box. Provide evidece where possible. Everyoe participates ad shares i the discussio process. Studets are workig together ad commuicatio is iteractive. The group is supportive of its idividual members. All members are active participats ad ecouraged to share ideas. 0 Evidece Group members ofte ask questios for clarificatio of elaboratio. The group discussio stays o topic or o directly related issues. The group is eergetic ad ethusiastic without beig a disruptio to other groups. Totals What was the best thig about the way this group worked together?

3 Name: Date: Period: Applicatios of Expoetial Fuctios The followig activities coicide with a series of video clips from Aytime you see this ico,, you should watch the idicated video segmet before proceedig. Be sure to aswer all questios that follow, showig all your work. WATCH THE INTRODUCTION AND VIDEO SEGMENT A GROWTH AND DECAY GRAPHS Exercises Sketch the graphs that represet expoetial growth ad expoetial decay o the followig grids. A microbiologist fids that the populatio of a virus will decrease by half every thirty miutes whe it is treated with a certai drug. There were 800 viruses i the iitial sample. a. Complete the table of values for the first three hours after this virus was treated with the drug. Time (Hours) Number of 800 Viruses b. Idetify the idepedet ad depedet variables.

4 c. Costruct a graph from the previous data. Be sure to label your axes. Draw a smooth, cotiuous curve through the poits. Attach your graph paper to this packet. d. Usig your graph, estimate the umber of viruses remaiig after 5 miutes. How may are left after hours 45 miutes? e. Explai whether or ot you thik the umber of viruses will evetually reach zero. ) $00 was ivested i a term deposit that compouded semi-aually (twice per year) ad paid 8% aual iterest. a. Fid the formula that represets the amout of the ivestmet at ay time. b. Complete the table of values, to the earest dollar for this ivestmet. Time (years) Amout (dollars) c. Draw a graph of your data o a piece of graph paper. Attach the paper to this packet. Be sure to label the axes. d. Usig your graph, estimate whe the origial ivestmet would triple i value. CHALLENGE Fifty bacteria double i populatio every 0 miutes. What equatio or formula Would describe this growth? CHALLENGE

5 WATCH VIDEO SEGMENT B GROWTH AND DECAY EQUATIONS 3) Write a equatio for the amout a ivestmet will be worth if $00 is ivested at 0% aual iterest compouded quarterly. 4) The world populatio reached 5.4 billio i 99 ad was icreasig at a rate of.6% each year. If this rate of growth is maitaied, write a equatio expressig the predicted populatio as fuctios of the umber of years sice 99. (Hit: 99 represets your iitial value!) 5) For every meter a diver desceds beeath the surface, the light itesity is reduced by 3%. Express the percet of surface light preset at ay give depth as a fuctio of the depth. 6) As river water passes through a filter, 0% of the uwated matter is removed. Express the percet, P, of uwated matter remaiig as a fuctio of the umber,, of filters used.

6 WATCH VIDEO SEGMENT C GROWTH AND DECAY Example: A laboratory sample iitially cotais 8000 g of radioactive substace. I four hours, there are 50 g of radioactive substace. Fid the half-life period for this sample. Solutio: I 4 hours, 5 half-life periods have occurred. Therefore, oe half-life period is 4/5 or 0.8 hours. 7) A techicia otes that a certai bacteria have a doublig period of 4 hours. If there is a iitial amout of 500 bacteria, how may will there be i 4 hours? 8) A radioactive substace has a half-life of 4 miutes. a. What percet of the origial amout of the substace remais after 8 miutes? b. What percet of the origial amout of the substace remais after 7 miutes?

7 WATCH VIDEO SEGMENT D CARBON-4 DATING As stated i the video, a formula used for carbo-4 datig is A A0 (0.5), where A is the amout of radioactivity i the give sample, A 0 is the amout of radioactivity i a moder relative sample ad is the umber of half-lives. The half-life of carbo-4 is approximately 5730 years. Example: The sample, A (mammoth rib), has 5% as much radioactivity as a related moder sample, A 0 (moder elephat rib). Fid the umber of half-lives of the sample. Solutio: A 5% 5% (0.5) 00% (0.5) 4 A (0.5) 0 00%(0.5) The sample has lived through half-lives, or (5730) =,470 years!! 0) The approximate age of a piece of charcoal foud at Stoehege is thought to be 4000 years old. What percet of radioactivity should be expected from a sample of this charcoal compared to a moder piece of charcoal if, the charcoal is 4000 years old?

8 Name: Date: APPLICATIONS OF EXPONENTIAL FUNCTIONS AT THIS STATION, YOU WILL BE CREATING A POSTER TO SUMMARIZE VARIOUS APPLICATIONS OF EXPONENTIAL GROWTH AND DECAY. ALL OF THE REQUIREMENTS ARE LISTED BELOW. A RUBRIC FOR YOUR POSTER GRADE IS ALSO INCLUDED. ) COMPLETE FX 89 & 90 IN YOUR NOTEBOOKS. HAVE THESE SOLUTIONS CHECKED PRIOR TO MOVING FORWARD WITH THE POSTER. ) EACH MEMBER OF THE GROUP IS RESPONSIBLE FOR ONE PART OF PROBLEM FX 87. YOU WILL DO A MINI-PRESENTATION TO THE OTHER MEMBERS OF YOUR GROUP ON HOW YOU ARRIVED AT YOUR SOLUTION. YOU ARE RESPONSIBLE FOR POSTING YOUR SOLUTION ON YOUR TEAM POSTER. POSTER REQUIREMENTS: ( poit each) ) Fid the time uit for your problem (days, weeks, years, etc.) ) State the appropriate multiplier. Be sure to show your work if ay calculatios are required for that multiplier. 3) Idetify the iitial value. 4) Write the expoetial equatio that represets your problem. 5) Sketch a graph, idetifyig key poits. BE SURE TO PUT YOUR NAME WITH THE PROBLEM YOU COMPLETED ON THE POSTER. ** Please ote: There are 6 parts to the problem. Each perso is resposible for 5 poits. This makes the poster worth a total of 30 poits!

9 FAST CARS WHAT S THE VALUE? FX 7 As soo as you drive a ew car off the dealer s lot the car is worth less tha what you paid for it. This is called depreciatio; so, you will sell it for less tha the price that you paid for it. Some cars depreciate more tha others (that is, at differet rates), but most cars depreciate. O the other had, some older cars actually icrease i value. This is called appreciatio. Suppose you have the followig choices for a car purchase: ) 999 Mazda Miata for $9,800 depreciates at % per year ) 996 Hoda Civic EX for $6,500 depreciates at 8% per year 3) 967 Ford Mustag for $4000 that is appreciatig at 0% per year Use the iformatio give above to complete the questios that follow. A) Clearly idetify the multiplier for each vehicle above. Be sure to show/ explai how you arrived at your aswer. B) Make a table that shows the value of each car after a give amout of time. Be sure to iclude the purchase price (iitial value) ad the value for the first 0 years. C) Write a fuctio for each car that idicates the value of the car i year. Be sure to label the fuctio with the ame of the car. D) Graph each of your fuctios o the same set of axes. Be sure to label ad scale the axes appropriately. Label each graph with the ame of the car.

10 E) Whe is the value of the Miata ad Civic the same? How ca you idetify this o your graph? F) Which of the cars is worth the most after 4 years? How ca you tell from your graph? Which car is worth the most after 5 years? After 0 years? G) Describe whe someoe would choose to buy the Miata over the Civic. Who would be most likely to purchase the Mustag? Which car would you buy? Why?

11 Name: Period: Date; Expoetial Fuctio Web Ivestigatio US POPULATION GROWTH: WHAT TO DO: Usig the resources provided below, fid the total US populatio for every decade from 790 to 990. Plot the data ad determie the expoetial fuctio to fit your data Calculate the percet icrease i populatio for each decade ad plot the data as a lie graph. Determie the three decades showig sigificat chages i the growth tred, ad research historical causes for the chages. TOOLS: Graphig calculator Computer Graph paper Ruler Pecil WEB RESOURCES US Cesus Bureau Select #, Urba ad Rural populatios USA: Outlie of America History A excellet site to begi research ito the historical, social, ad ecoomic reasos for the breaks i the growth of the populatio. STEPS TO FOLLOW ) Obtai the populatio figures for every decade from from the US Cesus Bureau. ) Record your data i a table usig Microsoft Excel. Be sure to label your colums with a headig. 3) Plot your data o a had-draw scatter plot. Clearly label the x axis with your idepedet variable ad the y axis with your depedet variable. 4) Draw a smooth curve of best fit through your poits. Fid the equatio of the expoetial fuctio that matches your curve. [ t( ) IV ( G) ] Be sure to show all your work to fid the equatio. 5) Calculate the percet icrease i total populatio for each decade usig your calculator ad the formula: ( recet figure) ( previous figure) previous figure 00 % icrease 6) Record your percet icrease data i a ew colum o your spreadsheet. 7) Usig Microsoft Excel, create a lie graph that shows the percet icrease over time. The year should be idepedet, the percet depedet. 8) Determie the three decades that show the greatest chages i growth treds. (Note: these do ot have to be icreases!) 9) Research historical causes for these tred chages usig the Outlie of America History. Be sure to properly documet ay resources used i your research.

12 SUBMIT A copy of your scatter plot with the equatio icluded. All work eeded to fid the equatio, eatly writte with all steps show. Percet Icrease calculatios. Spreadsheet ad lie graph saved to my teacher folder. Paragraph (miimum 4-5 seteces) describig the decades of major growth chages ad potetial causes.

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