Answers PBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Modeling with Exponential and Logarithmic Equations

Modeling with Exponential and Logarithmic Equations — Unit test Answers

25 verified answers2 views

Free Preview

What is the approximate value of ?

0.233

0.557

0.620

1.796

Free Preview

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 value of ?

–4

Negative one-fourth

One-fourth

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

For what value of n does ?

–3

Negative one-third

Five-ninths

What is the domain of ?

all real numbers less than –3

all real numbers greater than –3

all real numbers less than 3

all real numbers greater than 3

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

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 solution to

x = negative 95

x = negative 5

x = 5

x = 95

What is the solution to

x = negative 4

x = negative 2

x = 4

x = 8

What is the sum of the first seven terms of the geometric series?3 + 12 + 48 + 192 + ...

4,372

12,288

16,383

65,535

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)

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

What is the solution to the equation below?

mc008-2.jpg

mc008-3.jpg

mc008-4.jpg

mc008-5.jpg

If , what is the value of s?

–1

no solution

What is the solution of log2 (3x - 7) = 3?

One-third

Sixteen-thirds

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.

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.