Study Guide – Chapter 7



Study Guide – Unit 7 Name_______________________________

Exponential Functions – Algebra One L3 Block_______Date_____________________

Use this study guide to prepare for the Unit 7 test. Also re-work problems on quizzes, homework & problems from your notes. This study guide is due on the day of the test –and will NOT be accepted for credit after you take the test. (If you are absent for the test, it is due when you come to make up the test!). This is worth a 16 POINT homework grade. SHOW WORK FOR FULL CREDIT!!!

PROPERTIES OF EXPONENTS

A) Multiplication Properties of Exponents—Simplify each example below.

1) [pic] 2) (12x)[pic] 3) [pic]

4) (4r²s)²(-2s²)³ 5) (7x³y) [pic] 6) (3x)³(-5y)² 7) (-x³)²(x)²(-x[pic])³

B) Zero & Negative Exponents—Rewrite the expression with positive exponents.

8) m[pic] 9) [pic] 10) [pic] 11) [pic]

12) [pic] 13) [pic] 14) 6x[pic] 15) [pic]

C) Division Properties of Exponents—Simplify each expression below. Remember, the simplified expression should have no negative exponents.

16) [pic] 17) [pic] 18) [pic] 19) [pic]

D) Properties of Exponents—All Together. Simplify each expression below. Remember, the simplified expression should have no negative exponents.

20) [pic] 21) [pic] 22) 5[pic][pic]

23) 24)

F) Rational Exponents

When evaluating rational exponents you need to be very careful with negatives – is it the base or just taking the opposite of the result? Does it indicate a “position” change resulting in a fraction? Evaluate each of the following, no decimal answers please.

25) 163/2 26) 16-3/2 27) (-64)2/3 28) -642/3

29) -64 -2/3 30) 64 -2/3 31) (-64) -2/3 32) (-8) -1/3

Rewrite as Rational Exponents and then evaluate. If you have a decimal result, turn it into a fraction, if that is not possible, then round to the nearest hundredth.

33) [pic] 34) [pic] 35) [pic]

Simplify Rational Exponent Expressions completely

36) x2/3 (x4/3 37) (y1/6)3 38) [pic] 39) [pic]

40) (x1/2 ( x1/3)6 41) [pic] 42) [pic] 43)

44) 45) 46)

G) Exponential Growth & Decay Graphs—Identify each graph as growth or decay.

47) 48)

49) 50)

H) Applications of Exponential Growth & Decay

51) You buy a new car for $24,000. The value of the car decreases by 16% each year.

a)  Is this growth or decay? __________________________

b)  What is the initial value? __________________________

     c)  What is growth/decay rate?____________________________

    d)  What is the base/growth-decay factor for your function? _____________________

e) Write an exponential function equation for this car depreciation scenario:

    f)  What is the value of your car after 1 year? (show full value & reasonable rounded value)

   g)  What is the value of your car after 5 years?  (show full value & reasonable rounded value)

h) When will the value of your car be $8500? (show full value & reasonable rounded value)

52) You purchase an antique table for $875. Each year, the value of the table increases by 8%.

a)  Is this growth or decay? __________________________

b)  What is the initial value? __________________________

     c)  What is growth/decay rate?____________________________

    d)  What is the base/growth-decay factor for your function? _____________________

    e) Write an exponential function equation for this antique table scenario:

f) How much is the table worth in 5 years? (show full value & reasonable rounded value)

g) When will the table be worth $10,000? (show full value & reasonable rounded value)

I) Logistic Functions

52) Fruit Flies are placed in a half-pint milk bottle with a banana (for food) and yeast plants (for food and stimulus to lay eggs). Suppose that the fruit fly population after t days is given by

[pic]

a) What is the initial population of fruit flies? (show full value & reasonable rounded value)

b) What is the population of flies after 5 days? (show full value & reasonable rounded value)

c) What is the maximum number of fruit flies the milk bottle can support?

d) How long does it take the population to reach 180 fruit flies? (show full value & reasonable rounded value)

J) COMPOUND INTEREST – remember the two equations you can use are:

and A = Pert

53) You deposit $5000 in a bank account. Find the balance after 4 years for each of the following situations (show work – what your type in your calculator):

a) The account pays 3.5% annual interest compounded monthly.

b) The account pays 5.75% annual interest compounded quarterly.

c) The account pays 5% annual interest compounded yearly.

d) The account pays 4% interest compounded daily.

54) You deposit $900 in an account that pays 4.5% annual interest compounded continuously. What is the balance after 5 years? Show what you typed into your calculator.

55) In order to have $8500 in 7 years, how much do you have to put in your account that earns 5 ¾ % interest compounded weekly? Show work.

56) How long must you invest $12,000 in order for it to double in value in a savings bond that earns 8% interest compounded semi-annually? Show work/full value and reasonable answer.

K) Half Life - remember the equation to use is A(t) = A(1/2)t/h where t = time and h = length of the half life and A = original amount. For each problem show work or indicate what you did in your graphing calculator

57) An isotope of cesium (cesium-137) has a half life of 30 years. If 8.0 g of cesium-137 disintegrates over a period of 90 years, how many of grams of cesium-137 would remain?

58) Selenium-83 has a half life of 25 minutes. How many minutes would it take for a 10 mg sample to decay and have only 1.25 mg of it remain?

There will NOT be any exponential data questions on the test (so no exponential regression problems like the car project or other data questions)

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