1.  (07.01)

What is the solution to the equation 9(x – 2) = 27? (1 point)

 

x = 2.5

x = 0.5

x = –0.5

x = 3.5

2.  (07.01)

What is the solution to the equation   = 4(m + 2)? (1 point)

 

m =– 

m =– 

m =

m =3.  (07.01)

The value of a dirt bike decreases by 20% each year. If you purchased this dirt bike today for $500, to the nearest dollar how much would the bike be worth 5 years later? (1 point)

 

$84

$119

$164

$222

4.  (07.01)

What is the exponential function modeled by the following table?

x f(x)2 53 94 17(1 point)

 f(x) = 2x

f(x) = 2x + 1

f(x) = 3x

f(x) = 3x + 1

5.  (07.01)

The frog population at a lake doubles every three weeks. The population can be modeled by f(x) = 15(2)x and f(6) = 960. What does the 15 represent? (1 point)

 

The population after six weeks

The starting population

The rate the population increases

The number of weeks that have passed

6.  (07.01)

The amount of a radioactive isotope decays in half every year. The amount of the isotope can be

modeled by f(x) = 346(   )x and f(1) = 173. What does the 173 represent? (1 point)

 

The starting amount of the isotope

The amount of the isotope after one year

The rate the isotope decreases

The number of years that have passed

7.  (07.01)

The population of a species of rabbit triples every year. This can be modeled by f(x) = 4(3)x and f(5) = 972. What does the 3 represent? (1 point)

 

The starting population of the rabbits

The population of the rabbits after five years

The rate the population increases

The number of years that have passed

8.  (07.01)

A painting is purchased for $350. If the value of the painting doubles every 5 years, then its value is given by the function V(t) = 350 • 2t/5, where t is the number of years since it was purchased and V(t) is its value (in dollars) at that time. What is the value of the painting ten years after its purchase? (1 point)

 $1,000

$1,400

$1,800

$2,000

9.  (07.01)

Wes has been tracking the population of a town. The population was 3,460 last year and has been increasing by 1.35 times each year. How can Wes develop a function to model this? (1 point)

 

f(x) = 3460(1.35)x where 1.35 is the rate of growth

f(x) = (3460 • 1.35)x where 1.35 is the rate of growth

f(x) = 1.35(3460)x where 3460 is the rate of growth

f(x) = 3460(x)1.35 where 3460 is the rate of growth

10.  (07.01)

A savings account compounds interest, at a rate of 22%, once a year. George puts $750 in the account as the principal. How can George set up a function to track the amount of money he has? (1 point)

 

A(x) = 750(1 + .22)x where .22 is the interest rate

A(x) = 750(22)x where 22 is the interest rate

A(x) = 750(.22)x where .22 is the interest rate

A(x) = 750(1 + 22)x where 22 is the interest rate

11.  (07.02)

What is the logarithmic function modeled by the following table?

x f(x)8 316 432 5(1 point)

 

f(x) = logx2

f(x) = log2x

f(x) = 2 log10x

f(x) = x log102

12.  (07.02)

If Joe wanted to create a function that modeled a base of 8 and what exponents were needed to reach specific values, how would he set up his function? (1 point)

 f(x) = x8

f(x) = log8x

f(x) = logx8

f(x) = 8x

13.  (07.02)

Express 64 = 4x as a logarithmic equation. (1 point)

 

log4x = 64

log464 = x

log644 = x

log64x = 4

14.  (07.02)

Express 32 = x as a logarithmic equation. (1 point)

 

log3x = 2

log32 = x

log23 = x

log2x = 3

15.  (07.02)

What is the solution of log2x + 3125 = 3? (1 point)

 

x = 

x = 1

x = 

x = 4

16.  (07.02)

What is the solution of log2x + 727 = 3? (1 point)

 

x = –2

x = 2

x = 3

x = 4

17.  (07.03)

Which of the following is equivalent to log432? (1 point)

 

0.4

2.5

1.726

8

18.  (07.03)

Which of the following is equivalent to log507 rounded to three decimal places? (1 point)

 

2.010

0.497

–0.615

–0.854

19.  (07.04)

Given the exponential function A(x) = P(1 + r)x, what value for r will make the function a decay function? (1 point)

 

r = –2.1

r = 2.1

r = 0

r = 0.1

20.  (07.04)

Given an exponential function for compounding interest, A(x) = P(1.01)x, what is the rate of change? (1 point)

 

0.01%

1%

1.01%

10%

21.  (07.04)

The function f(x) = 10(5)x represents the growth of a lizard population every year in a remote desert. Crista wants to manipulate the formula to an equivalent form that calculates every half-year, not every year. Which function is correct for Crista's purposes? (1 point)

 

f(x) = 10(52) 

f(x) =   (5)x

f(x) = 10(5)x

f(x) = 10(   )2x

22.  (07.04)

Phillip is using logarithms to solve the equation 63x = 18. Which of the following equations would be equivalent to his original expression? (1 point)

 

6 log 3x = log 18

3 log 6 = x log 18

x log 3 = 6 log 18

3x log 6 = log 18

23.  (07.04)

What is the solution to the equation 21 x – 3 = 14? (1 point)

 

x ≈ –2.133

x ≈ –1.846

x ≈ 3.867

x ≈ 4.154

24.  (07.04)

What is the solution to the equation 9 3x ≈7? (1 point)

 

x = 0.376

x = 0.295

x = –0.295

x = –0.376

25.  (07.04)

What is the logarithmic form of the equation e2x ≈1732? (1 point)

 

ln 1732 = 2x

log2x1732 = e

2 logxe = 1732

ln 2x = 1732

26.  (07.06)

Which of the following represents the graph of f(x) =   ? (1 point)

 

27.  (07.06)

What function is represented below?

 (1 point)

 

f(x) = 

f(x) =   + 2

f(x) = 

f(x) =   – 228.  (07.06)

Given four functions, which one will have the highest y-intercept?

f(x) g(x) h(x) j(x)

Blake is tracking hissavings account withan interest rate of 5%and a original depositof $6.

x g(x)1 62 83 12

j(x) = 10(2)x

(1 point)

 f(x)

g(x)

h(x)

j(x)

29.  (07.06)

Given four functions, place them in order of their y-intercept, from highest to lowest.

f(x) g(x) h(x) j(x)

g(x) = 3(20)x

Al is monitoring thedecay of a populationof fungi. It is reducingin half every four weeks.The population startedat 14.

x j(x)1 5.002 2.503 1.25

(1 point)

 

g(x), h(x), j(x), f(x)

h(x), j(x), g(x), f(x)

f(x), g(x), j(x), h(x)

j(x), g(x), h(x), f(x)

30.  (07.06)

For the graphed exponential equation, calculate the average rate of change from x = 0 to x = 1.

 (1 point)

 

3

4

31.  (07.06)

For the graphed exponential equation, calculate the average rate of change from x = 1 to x = 4.

 (1 point)

 

– 

– 

– 

– 32.  (07.06)

What transformation has changed the parent function f(x) = 3(2)x to its new appearance shown in the graph below?

 (1 point)

 

f(x) + 2

f(x) + 4

f(x + 2)

f(x + 4)

33.  (07.06)

What transformation has changed the parent function f(x) = (.5)x to its new appearance shown in the graph below?

 (1 point)

 f(x) – 2

f(x + 2)

f(x) + 1

–1 • f(x)

34.  (07.07)

Which of the following represents the graph of the function f(x) = log3(x+2)? (1 point)

 

35.  (07.07)

What function is graphed below?

 (1 point)

 

f(x) = log (x – 3)

f(x) = log (x + 3)

f(x) = log x + 3

f(x) = log x – 3

36.  (07.07)

Which graph represents the function f(x) = log10(x + 2)? (1 point)

 

37.  (07.07)

Using the graph of f(x) = log10x below, approximate the value of y in the equation 10y = 5.

 (1 point)

 

y ≈ 0.01

y ≈ 1.48

y ≈ 0.70

y ≈ –2.01

38.  (07.07)

Using the graph of f(x) = log2x below, approximate the value of y in the equation 22y = 4.

 (1 point)

 y ≈ 2

y ≈ 1

y ≈ 0.47

y ≈ 4.01

39.  (07.07)

What transformation has changed the parent function f(x) = log2x to its new appearance shown in the graph below?

 (1 point)

 

f(x + 3)

f(x – 3)

f(x) + 3

f(x) – 3

40.  (07.07)

What transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below?

 (1 point)

 

f(x – 2)

f(x + 2)

f(x) – 2

f(x) + 2

41.  (07.07)

What transformation has changed the parent function f(x) = log2x to its new appearance shown in the graph below?

 (1 point)

 

–2 • f(x)

2 • f(x)

f(x) – 2

f(x) + 2

42.  (07.08)

A heated piece of metal cools according to the function c(x) = (.5)x – 11, where x is measured in hours. A device is added that aids in cooling according to the function h(x) = –x – 3. What will be the temperature of the metal after five hours? (1 point)

 

–8° Celsius

26° Celsius

32° Celsius

56° Celsius

43.  (07.08)

A population of flies grows according to the function p(x) = 2(4)x, where x is measured in weeks. A local spider has set up shop and consumes flies according to the function s(x) = 2x + 5. What is the population of flies after two weeks with the introduced spider? (1 point)

 

15 flies

23 flies

32 flies

36 flies

44.  (07.08)

A video game sets the points needed to reach the next level based on the function g(x) = 8(2)x + 1, where x is the current level. The hardest setting promises to multiply the points needed in each level according to the function h(x) = 3x. How many points will a player need on the hardest setting of level 5? (1 point)

 

15 points

512 points

527 points

7680 points

45.  (07.08)

Given the function f(x) = 2x, find the value of f–1(32). (1 point)

 f–1(32) = 0

f–1(32) = 1

f–1(32) = 5

f–1(32) = 16

46.  (07.08)

Given the function f(x) = log3(x + 4), find the value of f–1(3). (1 point)

 

f–1(3) = 7

f–1(3) = 12

f–1(3) = 23

f–1(3) = 31