Chapter 4 Review Game Rules I will put up calculator and no calculator problems. If caught using a calculator on a no calculator problem, your team loses all of its points. Each member of the team with the most points at the end of class with get a homework pass.

Simplify the following without a radical symbol #1: No Calculator Simplify the following without a radical symbol

#1: Answer (8x3y12z9)1/3 81/3 ∙ x3/3 ∙ y12/3 ∙ z9/3 2xy4z3

Evaluate the following #2: No Calculator Evaluate the following

#2: Answer 1/16

#3: No Calculator Write an equivalent equation for A = BC2 using ln A in terms of ln B and lnC.

#3: Answer lnA = lnB + 2lnC

Solve ln t = 0.14 to the nearest hundredth. #4: Calculator Solve ln t = 0.14 to the nearest hundredth.

#4: Answer e0.14 = 1.15

#5: Calculator A bank account starts with $4800 with an interest rate of 6.75% compounded monthly. How much money (to the nearest penny) is in the account at the end of five years?

#5: Answer 4800(1 + .0675/12)12*5 = $6720.55

#6: Calculator In 1989, Vermont had a population of 567,000 people. The state was growing at 1.2% annually. At this rate of growth, in what year would Vermont reach a population of 600,000 people?

#6: Answer 567000*e0.012x = 600000 e0.012x = 600/567 ln (600/567)/0.012 = x x = 4.71 years 1989 + 5 = 1994

#7: No Calculator Between what two integers is log387?

Between 4 and 5 #7: Answer because 34 = 81 and 35 = 243,

#8: No Calculator Evaluate the following: -3/4

#8: Answer 8/27

#9: No Calculator Evaluate the following logarithm.

#9: Answer 1/3

#10: Calculator Solve for x to the nearest hundredth. 32x = 38

#10: Answer Log3 38 = 2x Log3 38 = x 2 x = 1.66

#11: Calculator Polonium-200 has a half-life of 140 days. How many grams (to the nearest hundredth) would be left after one year if you started with 200 grams?

#11: Answer y = abx y = 200(.5)365/140 y= 32.82g

#12: Calculator Solve for n to the nearest thousandth. 21(12)n = 5556

#12: Answer n = 2.245 12n = 5556/21 log12(5556/21) = n

#13: No Calculator log480 – log45 Evaluate the following logarithm using properties learned in this chapter. log480 – log45

#13: Answer log4(80/5) = log416 = log4(42) = 2

#14: No Calculator logt x = logt s – 3logt r Write the following equation without logarithms. logt x = logt s – 3logt r

#14: Answer logtx = logt (s/r3) x = s/r3

#15: No Calculator Use the fact that log54 = .8614 to help calculate the following logarithm. log520

#15: Answer log5(5*4) = log55 + log54 = 1 + .8614 = 1.8614

#16: Calculator Solve the following equation for x to the nearest thousandth. 5x = 2.413

#16: Answer log52.413 = x log 2.413 = x log 5 x = 0.547

#17: Calculator A savings account is started with $10,000. It is continuously compounded at 9.75% interest. How many years (to the nearest tenth) will it take for the account balance to triple in value?

t = 11.3 years #17: Answer 30000 = 10000e.0975t 3 = e.0975t ln 3 = .0975t t = ln 3/ .0975 t = 11.3 years

#18: Calculator Solve the following equation for b to the nearest thousandth. logb 35 = 3

#18: Answer b3 = 35 b = 351/3 b = 3.271

#19: No Calculator Simplify the following expression

#19: Answer ln e-3 = -3

#20: No Calculator Write the following as one logarithm.

#20: Answer log3b3/2 - log3c4 log3 (b3/2/c4)

Simplify the following expression #21: No Calculator Simplify the following expression

#21: Answer log6 (1/63) =log66-3 = -3

f(x) = log6x #22: No Calculator Write an equation for the inverse of the following function. f(x) = log6x

#22: Answer f-1(x) = 6x

#23: Calculator $800 is put in a savings account at the birth of a child. The account earns 10% continuously compounded. How much money is in the account (to the nearest penny) on the child’s 21st birthday if no money is deposited or withdrawn?

#23: Answer y = 800e0.10*21 y = $6532.94

#24: Calculator Calculate the following log to the nearest tenth. log319

#24: Answer log 19 = ln 19 log 3 ln 3 2.7

#25: Calculator A biologist finds the number of species S on an island is related to the area A of the island. Use the following equation to determine the area of the island (to the nearest square mile) if there are 420 species on the island. S = 28.3A0.39

#25: Answer 420 = 28.3A0.39 (420/28.3) = A39/100 (420/28.3)100/39 = A A = 1009 mi.2

#26: Calculator Find the domain and range of the following function: g(x) = 8x – 7

Domain: All Real Numbers Range: All Real Numbers > -7 #26: Answer The graph of 8x - 7 is the graph of 8x shifted down seven units. This means the horizontal asymptote is also shifted down seven units. Domain: All Real Numbers Range: All Real Numbers > -7