Geometric Series — Unit test Answers

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The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as , where and is the least intense sound a human ear can hear. What is the approximate loudness of a rock concert with a sound intensity of 10–1?

2 Db

22 Db

60 Db

110 Db

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What is the range of the function

y less-than 0

y greater-than 0

y less-than 4

y greater-than 4

What is the approximate value of ?

0.233

0.557

0.620

1.796

What is the true solution to the equation below?

and

The range of which function is ?

y = 2x

y = 2(5x)

y = 5x +2

y = 5x + 2

What is the solution to

x = negative 4

x = negative 2

x = 4

x = 8

For what value of x does ?

–9

–3

The population, p, of a town after t years is represented using the equation . Which of the following is an equivalent expression?

Option

Which equation is represented by the graph below?

y = l n x minus 3

y = l n x minus 4

y = e Superscript x Baseline minus 3

y = e Superscript x Baseline minus 4

The formula for determining the frequency, f, of a note on a piano is , where h is the number of half-steps from the A above middle C on the keyboard. A note is six half-steps away from the A above middle C. The frequency of the A above middle C is 440 Hz. How much greater is the frequency of the new note compared with the frequency of the A above middle C?

29.3%

41.4%

70.7%

182.3%

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equation represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number.

1 year

2 years

5 years

8 years

A painter is painting a wall with an area of 150 ft2. He decides to paint half of the wall and then take a break. After his break, he paints half of the remaining unpainted portion and then takes another break. If he continues to paint half of the remaining unpainted portion between breaks, approximately what portion of the original wall will be painted when he takes his fifth break?

112.50 ft2

145.31 ft2

147.66 ft2

290.63 ft2

Which geometric series converges?

StartFraction 1 Over 81 EndFraction + StartFraction 1 Over 27 EndFraction + one-ninth + one-third + ellipsis

1 + one-half + one-fourth + one-eighth + ellipsis

Sigma-Summation Underscript n = 1 Overscript infinity EndScripts 7 (negative 4) Superscript n minus 1

Sigma-Summation Underscript n = 1 Overscript infinity EndScripts one-fifth (2) Superscript n minus 1

If the equation below is solved by graphing, which statement is true?

The curves intersect at approximately x = 0.46.

The curves intersect at approximately x = 0.75.

The curves intersect at approximately x = 1.11.

The curves intersect at approximately x = 3.07.

What is the true solution to the logarithmic equation below?

x = 0

x = two-ninths

x = four-ninths

x = two-thirds

For what value of n does ?

–3

Negative one-third

Five-ninths

The magnitude, M, of an earthquake is defined to be , where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. What is the magnitude of an earthquake that is 35 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.