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College Algebra and the TI-83 Lesson #13 Exponential functions I

By Louis Nelson,2014-05-15 18:23
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College Algebra and the TI-83 Lesson #13 Exponential functions I

    College Algebra and the TI-83

    Lesson #13

     Exponential functions

    I. Graphs of Exponential Functions.

    xybwherebisanumber,b0andb1

     x EXPONENTIAL GROWTH: y?b, b > 1

    x EXPONENTIAL DECAY: y?b, 0 < b < 1

    xx1??xeY?3Exercise 1. Consider the functions , , Y3= Y???122??a) Input them Y1, Y2, Y3 in the calculator.

? Y= (all Plots should be off) , type

    xx1??xeY?3? ? ? Y3= Y???122??nd? 2 QUIT

b) Evaluate Y1(3), Y2(-4), Y3(1.8), Y3(-2.3)

? VARS ? Y-VARS 1: Function 1:Y1

    ? Y1(3) ENTER answer: 27

    ? VAR ? Y-VARS 1: Function 2

    ? Y2(-4) ENTER answer: 16

    ? VAR ? Y-VARS 1: Function 3

    ? Y3(1.8) ENTER answer: 6.049647464

    ? VAR ? Y-VARS 1: Function 3

    ? Y3(-2.3) ENTER answer: 0.1002588437

     ndc) Graph the functions Y1, Y2, Y3. Use TRACE and 2 TABLE to obtain points on the graph.

? WINDOW Xmin=-10 Xmax=10 Ymin=-5 Ymax= 40

    ? blue Y= nd? Select Y1 = 3^x (deselect Y2 and Y3) GRAPH TRACE 2 TABLE nd? Select Y2 = (1?2)^x (deselect Y1 and Y3) GRAPH TRACE 2 TABLE nd? Select Y3 = e^x (deselect Y1 and Y2) GRAPH TRACE 2 TABLE

    -64-

    1nd both by using the number e in 2 e and using the Exercise 2. Evaluate 3e

    xexponential function y=. end? 1 ? MATH 4 2 e ) ENTER answer: 0.7165313106

    ndx? 2 ^(-1 ) ENTER answer: 0.7165313106 e?3

    1x?1Exercise 3. Solve the equation . Give answer as a fraction. 8?4? MATH 0 ? CLEAR eqn: 0=8^(x+1) 1?4 ENTER ? x= 1 (any guess) ALPHA SOLVE answer: x=-1.6666666 nd? 2 QUIT

    ? x ENTER

    ? MATH 1 ENTER answer: x=-5/3

    x?1Exercise 4. Solve the equation 5?10.

? MATH 0 ? CLEAR eqn:0= 5^(x+1)-10 ENTER

    ? x= 1 (any guess) ALPHA SOLVE answer: x=.43067655807 nd? 2 QUIT

    x?1xExercise 5. Solve the equation 3?2. Give answer as a fraction.

    ? MATH 0 ? eqn: 0=3^(x+1) 2^x ENTER ? x= 1 (any guess) ALPHA SOLVE ans.: x=-2.709511291 nd? 2 QUIT

    ?|x?1|Exercise 6. Graph the function y = 2

? WINDOW Xmin=-5 Xmax=5 Ymin=-.5 Ymax=3

    ? Y= select Y1=2^-abs(x+1) ENTER GRAPH

     Note: abs can be obtained from the CATALOG key

    x3??Exercise 7. Graph the function f(x)=and its inverse. f(x)? ??2??? WINDOW Xmin = -5 Xmax = 5 Ymin = -5 Ymax=10

    ? Y Y3= (3?2)^x ENTER GRAPH nd? 2 DRAW 8 VARS Y-VARS 1 3 ENTER

    -65-

Exercise 8. Suppose $5000 is invested at an annual interest rate of 8%. Compute the

    balance after 15 years if interest is compounded monthly. Use the formula given below.

    Check by using FINANCE

    ktr??, P=$5000, r=8, k=12, t=15 Formula: B(t)?P1???k??P=5000, r =0.08 , t=15, k=12

? 5000 ? (1 + 0.08 ? 12)^(12 ? 15) ENTER

    ? ? answer: 16534.61

    Check: nd? TI-83: 2 FINANCE 1: TVM Solver

    ? TI-83 Plus: APPS 1: FINANCE TVM Solver

    ? N=15 I%=8 PV=-5000 PMT=0 FV=10000 (or any other guess) ?12

    ? P/Y=12 C/Y=12 PMT: END

    ? (go back to FV) ALPHA SOLVE answer: 16534.61

Exercise 9. In exercise 8, in how many years will the original money of $5000 double.

    P=$5000, B=$10000, r=8%, n=12, find t. nd FINANCE 1: TVM Solver change FV=10000 ? TI-83: 2

     TI-83 Plus: APPS 1: FINANCE TVM Solver

    ? move back to N=180 ALPHA SOLVE answer: 104.3182669

    ? 104.3182669 ? 12 ENTER answer: 8.69 years

Exercise 10. In exercise 8, what is the balance after 15 years, if the money is

    compounded continuously?

    rtB(t)?PeFormula: P = 5000, r = 8%, t = 15 xnde? 5000 ? 2 (.08?15) ENTER answer: 16600.58 Check answer nd? TI-83: 2 FINANCE 1: TVM Solver

     TI-83 Plus: APPS 1: FINANCE TVM Solver

    ?? N=15 EE10 (or any large number) I% = 8 PV = -5000 PMT = 0

     FV =1 0000 (or any other guess)

    ? P/Y = EE10 C/Y = EE10 PMT: END

    ? (go back to FV) ALPHA SOLVE answer: 16600.58

    -66-

Exercise 11. Repeat exercise 9 if the money is compounded continuously. nd FINANCE 1: TVM Solver ? TI-83: 2

    ? TI-83 Plus: APPS 1: FINANCE TVM Solver

     change C/Y EE10 (any large number)

    ? Move back to N ALPHA SOLVE answer: 8.66E10

    ? 8.66E10?E10 answer: 8.66 years

Exercise 12. What is the monthly payment for an $18,000 car if it is financed at 7.5%

    annual interest for 5 years?

    Pim?Formula: , P=18000, i=0.075/12, N=60 months ?N1?(1?i)

    ? (18000 ? (0.075 ? 12)) ? (1 (1 + 0.075?12)^(-60)) ENTER

     answer: 360.68

    Check answer nd? TI-83: 2 FINANCE 1: TVM Solver

     TI-83 Plus: APPS 1: FINANCE TVM Solver

    ? Enter N=60 I%=7.6 PV=18000 PMT=-100 (any guess)

    ? FV=0 P/Y==12 C/Y=12 PMT: END

    ? go back to PMT ALPHA SOLVE answer: 361.54

Exercise 13. In problem 12, if a person can only afford a $300 monthly payment, what is

    the maximum value that he can pay for a car? nd? TI-83: 2 FINANCE 1: TVM Solver ? TI-83 Plus: APPS 1: FINANCE TVM Solver

    ? enter N=60 I%=7.6 PV=10000 (any guess) PMT=-300 FV=0 P/Y=12

    C/Y=12 PMT: END

    ? go back to PV ALPHA SOLVE answer: 14936.15

Exercise 14. In problem 12, if the person makes a $400 payment each month, in how

    many months is the $18000 car paid? nd? TI-83: 2 FINANCE 1: TVM Solver

     TI-83 Plus: APPS 1: FINANCE TVM Solver

    ? enter N=60 I%=7.6 PV=18000 PMT=-400 FV=0 P/Y=12 C/Y=12

    PMT: END

    ? go back to N ALPHA SOLVE answer: 53.13693929 payments

    -67-

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