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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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.

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Which is the graph of ?

On a coordinate plane, a curve starts at y = negative 3 and curves up into quadrant 1. It approaches y = 3.

On a coordinate plane, a curve starts at y = negative 2 and curves up into quadrant 2. It approaches y = 2 in quadrant 2.

On a coordinate plane, a curve starts at y = 3 and curves down into quadrant 4. It approaches y = negative 3 in quadrant 4.

On a coordinate plane, a curve starts at y = 4 and curves down into quadrant 3. It approaches y = negative 3 in quadrant 3.

How does the value of compare with the value of ?

The value of is about 4 times the value of .

The value of is about times the value of .

The value of is about 3 times the value of .

The value of is about times the value of .

What is the range of the function

all real numbers less than –1

all real numbers greater than –1

all real numbers less than 1

all real numbers greater than 1

The height of a plant over time is shown in the table below. Using a logarithmic model, what is the best estimate for the age of the plant when it is 19 inches tall?Plant Heightt, time in monthsh, height in inches118218.21318.33418.42518.48618.54

10 months

14 months

16 months

28 months

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.

A population of insects increases at a rate of 1.5% per day. About how long will it take the population to double?

2.5 days

5.0 days

46.6 days

66.7 days

What is the solution to the equation

mc012-2.jpg

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mc012-4.jpg

mc012-5.jpg

Which graph represents an exponential decay function?

On a coordinate plane, a curve opens up and to the right in quadrant 4.

On a coordinate plane, a curve opens up and to the right in quadrants 1 and 2. The line rapidly decreases in quadrant 2 and then curves and approaches the x-axis in quadrant 1.

On a coordinate plane, a line slightly curves up in quadrant 1.

On a coordinate plane, a line slowly increases in quadrant 2 and then increases rapidly into quadrant 1.

The range of which function is ?

y = 2x

y = 2(5x)

y = 5x +2

y = 5x + 2

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 domain of the function graphed below?

mc023-2.jpg

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Which expression is equivalent to ?

4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x times 1)

4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline StartFraction x cubed Over 2 EndFraction minus 5 log Subscript 12 Baseline 1

log Subscript 12 Baseline 4 x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x) + 1

4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x + 1)

A city manager made the graph below to represent the number of passengers that city buses can carry, where the number of passengers is represented by x, and the number of buses by y.If all city buses carry the same number of passengers, what is the least number of buses needed to carry 710 passengers?

What are the domain and range of the step function below?

domain = {all real numbers}, range = {all real numbers}

domain = {all real numbers}, range = {...–4, –1, 2, 5, ...}

domain = {...–5, –2, 1, 4, ...}, range = {...–4, –1, 2, 5, ...}

domain = {all integers}, range = {all real numbers}

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

What is the range of the function

y less-than 0

y greater-than 0

y less-than 4

y greater-than 4

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.