1. anonymous

Belinda wants to invest $1000. The table below shows the value of her investment under two different options for three different years: Number of years 1 2 3 Option 1 (amount in dollars) 1300 1690 2197 Option 2 (amount in dollars) 1300 1600 1900 Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points) Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points) Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points) 2. anonymous @saseal last one :) 3. anonymous lemme study this wall of text 4. anonymous okay dookie 5. anonymous Part A is asking about linear and exponential function, you know the different between em right? 6. anonymous Yes ma'am/sir 7. anonymous im doge xD 8. anonymous so a guyyy??? Like I am really slow btw 9. anonymous you can prolly guess which one is a linear function and exponential just by looking 10. anonymous maybeee??? 11. anonymous i can but i dont know about you 12. anonymous option one is exponential and option 2 is linear 13. anonymous possibly OS makes me feel really stupid 14. anonymous you are correct 15. anonymous but for the explanation part 16. anonymous option two is linear because it increases by a fixed amount? 17. anonymous its describing the difference between this 2 functions. btw “Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.” - Albert Einstein 18. anonymous yea 19. anonymous okay so "option two is linear because it increases by a fixed amount" 20. anonymous yea 21. anonymous I am not sure about option one though 22. anonymous when you did the last question, exponential increase by what factor? 23. anonymous the f(x) of your last question 24. anonymous 3% 25. anonymous its a power right? 26. anonymous 0.69*1.03^x 27. anonymous its a compounding 3% 28. anonymous yes...but this question doesn't have an equation. 29. anonymous yea that f(x) is an exponential equation just like option 1 30. anonymous whatt? 31. anonymous they behave the same way 32. anonymous like this on the graph|dw:1438877568681:dw| 33. anonymous they have different flavors but they increase to a very steep gradient in the end 34. anonymous increase or decrease depends on the function 35. anonymous they dont behave like a linear function which looks like this on the graph|dw:1438877675414:dw| 36. anonymous okayy sooo... 37. anonymous option b has a quantity growth proportional to its current value 38. anonymous thats what makes it exponential 39. anonymous option a you mean? 40. anonymous yea 41. anonymous Part B now? 42. anonymous Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. 43. anonymous option 2 first: its y=mx+b option 1: you want me to hand you compound interest formula? 44. anonymous what? I know y=mx+b. But how does that apply to this? and yes please 45. anonymous y=mx+b b is your y-intercept where its year 0 which is 1000. now from there what is the rate of change of the$ per year? that will be your m

46. anonymous

okay. Help?

47. anonymous

compound interest formula$A=P(1+\frac{ r }{ 100 })^n$

48. anonymous

A=amount accumulated P=principal amount r=interest rate n=years

49. anonymous

yes I know that we were taught this: f(x)=p(1+r)^x where r was the rate in decimal form, p was principle and x was x

50. anonymous

51. anonymous

okay

52. anonymous

now lets find your m with 2 points

53. anonymous

ok, what about 1 and 0

54. anonymous

0 is year 0, whats your $at year 0? 55. anonymous for option B?its 1000 56. anonymous now year 1 of option b? 57. anonymous 1300 58. anonymous now you have your 2 points (0,1000) and (1,1300) 59. anonymous you can find your slope from here 60. anonymous $m=\frac{ y_2-y_1 }{ x_2-x_1 }$ 61. anonymous 1300-1000/1-0 62. anonymous yes 63. anonymous 300/1 or 300 64. anonymous nvm ill show you the simple interest formula so you dont get confused 65. anonymous okay? 66. anonymous $I=P \times R \times T$ 67. anonymous OKOKOKOk wut? 68. anonymous interest rate is $\frac{ 1300-1000 }{ 1000 } \times 100$ I = interest created P = principal R = interest rate T = time 69. anonymous 300/1000*100=30 70. anonymous yup 71. anonymous we are still on part B? 72. anonymous right? 73. anonymous yes 74. anonymous okay. What was that the answer to? 30 75. anonymous now we are support to create function 76. anonymous okay so f(x)=300 77. anonymous lol 78. anonymous we piece the part of the simple interest formula + principal to get the answer 79. anonymous like this f(x)=x+(P*R*T) 80. anonymous ok 81. anonymous oops its f(x)=1000+(1000*R*x) 82. anonymous since x is time which is the only thing that changes 83. anonymous test this function see if it works 84. anonymous So the answer to part B for Option 2<< or 1 am not sure is f(x)=1000+(1000*R*x) 85. anonymous lets see...$f(1)=1000+(1000*0.3*1)=1300$$f(2)=1000+(1000*0.3*2)=1600$ 86. anonymous thats good for your part b option 2 87. anonymous for option 1 its the compound interest formula, you can find your interest rate like this$\frac{ 1300-1000 }{ 1000 } \times 100$ 88. anonymous $f(x)=1000(1.3)^x$ 89. anonymous "f(1)=1000+(1000∗0.3∗1)=1300 f(2)=1000+(1000∗0.3∗2)=1600" for option b? 90. anonymous nah its $f(x)=1000+(1000*0.3*x)$you can simplify it further if you like to 91. anonymous well its an essay q, I do not know what its asking for, but I gave the specific question 92. anonymous they say write function, you cant write an essay on that 93. anonymous not literal essay, I mean its not graded by the computer, its by the teacher, so I am not sure what specifically the answer is, since ther are no multiple choice. 94. anonymous they are asking you to craft a function that whenever you put in a year, it will churn out something that tells you the$ you get when you put your \$ in for that amount of year

95. anonymous

okay moving on. Option A?

96. anonymous

scroll up abit

97. anonymous

okay. Part C?

98. anonymous

Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option.

99. anonymous

now plug in 20 into both functions and see the difference

100. anonymous

where is the n in the function for option 1? f(x)=1000(1.3)x WOAH WOAH WOAH JUST TO GET THIS ALL CLEAR, OPTION 2: f(x)=1000+(1000*0.3*n) OPTION 1:f(x)=1000(1.3)x

101. anonymous

yea

102. anonymous

Option 1:$f(x)=1000(1.3)^x$Option 2:$f(x)=1000+(1000*0.3*x)$

103. anonymous

OKAY so next, we fill in 20 f(x)=1000*190.049637749

104. anonymous

190049.637749

105. anonymous

yea no problem

106. anonymous

now compare that to option 2

107. anonymous

f(x)=1000+(1000∗0.3∗20) 7000 and

108. anonymous

190049.637749 and 7000

109. anonymous

whats 190049.637749-7000

110. anonymous

183049.638

111. anonymous

now you got your numbers go explain it

112. anonymous

do you think 180349.638 is a signifcant difference?

113. anonymous

yeahhh

114. anonymous

thanks for the help :)

115. anonymous

yw