MATH Week 6 DQ

Advanced Functions

1) Solve: 4096x = 8 1)

2) Solve: 1 9

x = 729 2)

3) Solve: 4 7

x = 2401

256 3)

4) Solve: 4-x = 1 256

4)

5) Solve: 4(8 - 2x) = 256 5)

6) Solve: 3(6 - 3x) = 1 27

6)

7) Solve: 3(6 + 3x) = 1 27

7)

8) Solve: 4 = b2/3 8)

9) Solve: a3/4 = 125 9)

10) Solve: 25 9

x+1 = 3

5 x-1

10)

11) Solve: e4x - 1 = (e3)-x 11)

12) Solve: 8x - 1 = 323x 12)

13) Solve: m-4 = 1 81

13)

14) Solve: 1 3

2x + 3 = 9x- 5 14)

1

15) Solve: ( 5 )x + 1 = 25x 15)

16) Solve: ex - 3 = 1 e6

x + 2 16)

17) The growth in the mouse population at a certain county dump can be modeled by the exponential function A(t)= 906e0.012t, where t is the number of months since the population was first recorded. Estimate the population after 36 months.

17)

18) The decay of 938 mg of an isotope is given by A(t)= 938e-0.022t, where t is time in years since the initial amount of 938 mg was present. Find the amount (to the nearest milligram) left after 96 years.

18)

19) The sales of a mature product (one which has passed its peak) will decline according to the function S(t) = S0e-at, where t is time in years since the peak sales. Find the sales of a product 17 years after its peak sales if a = 0.22 and S0 = 77,500.

19)

20) The number of reports of a certain virus has increased exponentially since year 0. The number of cases can be approximated using the function r(t) = 119 e0.008t, where t is the number of years since year 0. Estimate the number of cases in year 40.

20)

21) An element decays at the rate of S(t) = se-0.048t, where s is the initial amount in grams and t is the time in years since this initial amount was present. If you have a 71-gram piece of this element, how many grams will you have 5 years from now? Round your answer to the nearest tenth of a gram.

21)

22) Solve: log5 125 = x 22)

23) Solve: log3 1

27 = x 23)

24) Solve: log7 712 = x 24)

25) Solve: log x 625 = 4 25)

2

26) Solve: x = 8 log8 13 26)

27) Solve: x = log10 0.01 27)

28) Solve: x = log2 5

8 28)

29) Solve: logx 9 = - 2 29)

30) Solve: log4 x = 3 30)

31) Solve: log5 x = -3 31)

32) Solve: log(x - 5) 10 = 1 32)

33) Solve: log(x + 7) 11 = 1 33)

34) Solve: 8x - 32 = logx 1 34)

35) Suppose f(x) = logax and f(4) = 2. Find f(16). 35)

36) Suppose f(x) = logax and f(4) = 2. Find f 1

16 . 36)

37) Suppose f(x) = loga(x) and f(7) = 2. Find f(343). 37)

38) Suppose f(x) = loga(x) and f(5) = 2. Find f 5

5 38)

39) Evaluate: 100log107 39)

40) Evaluate: log10(0.01)9 40)

41) Evaluate: 1000log1010 41)

42) Evaluate: log10(0.0001)10 42)

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43) The growth in population of a city can be seen using the formula p(t) = 2148e0.008t, where t is the number of years. Use this formula to calculate the population after 10 years.

43)

44) Suppose the government wants to impose a tax on fossil fuels to reduce carbon emissions. The cost benefit is modeled by ln(1 - P) = -0.0039 - 0.0051x, where x represents the dollars of tax per ton of carbon emitted and P represents the percent reduction in emissions of carbon. (P is in decimal form.) Determine P when x = 63. Round to three decimal places.

44)

45) Suppose f(x) = 32.6 + 1.2log (x + 1) models salinity of ocean water to depths of 1000 meters at a certain latitude. x is the depth in meters and f(x) is in grams of salt per kilogram of seawater. Approximate the salinity (to the nearest hundredth) when the depth is 771 meters.

45)

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Answer Key Testname: FORUM ADVANCED FUNCTIONS

1) 1 4

2) {-3} 3) {-4} 4) {4} 5) {2} 6) {3} 7) {-3} 8) {-8, 8} 9) {625}

10) - 1 3

11) 1 7

12) - 1 4

13) {-3, 3}

14) 7 4

15) 1 3

16) - 9 7

17) 1396 18) 113 19) 1841 units 20) 164 cases 21) 55.9 g 22) {3} 23) {-3} 24) {6} 25) {5} 26) {13} 27) {-2}

28) 3 5

29) 1 3

30) {64}

5

Answer Key Testname: FORUM ADVANCED FUNCTIONS

31) 1 125

32) {15} 33) {4} 34) {4} 35) 4 36) -4 37) 6 38) -1 39) 49 40) -18 41) 1000 42) -40 43) 2327 44) 0.278 45) 36.07 g/kg

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