Answers PBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Modeling with Exponential and Logarithmic Equations

Modeling with Exponential and Logarithmic Equations — Unit test Answers

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Which function is shown in the graph below?

y = (one-half) Superscript x + 3 Baseline minus 1

y = (one-half) Superscript x minus 3 Baseline + 1

y = (one-half) Superscript x minus 1 Baseline + 3

y = (one-half) Superscript x + 1 Baseline minus 3

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Which graph shows the solution to the equation below?

On a coordinate plane, 2 curves intersect at (1, 0).

On a coordinate plane, a line intersects with a curve.

On a coordinate plane, a line with positive slope and a curve are shown.

On a coordinate plane, 2 hyperbolas are shown.

What is the approximate value of ?

0.233

0.557

0.620

1.796

The range of which function is ?

y = 2x

y = 2(5x)

y = 5x +2

y = 5x + 2

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%

If you are given the graph of , how could you graph ?

Translate each point of the graph of h(x) 3 units up.

Translate each point of the graph of h(x) 3 units down.

Translate each point of the graph of h(x) 3 units right.

Translate each point of the graph of h(x) 3 units left.

What is the true solution to the logarithmic equation below?

x = 0

x = two-ninths

x = four-ninths

x = two-thirds

Which of the following is true about the base b of a logarithmic function?

b > 0 and b = 1

b > 0 and

b < 0 and

b < 0 and b = 1

A radioactive element has a half-life of six days. What is the approximate decay rate of the element after the first day?

0.9%

1.5%

8.3%

10.9%

An equation for the depreciation of a car is given by y = A(1 – r)t , where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?

3.3 years

5.0 years

5.6 years

6.6 years

For what value of x does ?

–9

–3

Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. After c years, Calvin has $658.80. Makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. After m years, Makayla has $613.04. What is the approximate difference in the number of years that Calvin and Makayla have their money invested?

Makayla invests her money 1 year longer.

Makayla invests her money 2 years longer.

Calvin invests his money 1 year longer.

Calvin invests his money 2 years longer.

Which of the following shows the extraneous solution to the logarithmic equation below?

x = negative 16

x = negative 8

x = negative 4

x = negative 2

What is the range of the function

y less-than 0

y greater-than 0

y less-than 4

y greater-than 4

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.

–1.5

–0.5

1.5

3.6

The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation , where I is the intensity of a given sound and is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when ?