Riley is analyzing the decay of a chemical substance, which can be modeled by the function f(x) = -2 \log_2 x + 2. Based on the graph, which of the following describes the features of this function?

The function has a vertical asymptote at x = 0, decreases as x increases, and has a y-intercept at (1, 2).

The function has a vertical asymptote at x = 2, increases as x increases, and has a y-intercept at (0, 2).

The function has a horizontal asymptote at y = 0, increases as x increases, and has a y-intercept at (2, 0).

The function has a vertical asymptote at x = 1, decreases as x increases, and has a y-intercept at (0, 2).

Riley is studying the temperature of a cooling object over time, which can be modeled by the function f(x) = $$(1/3)^{x} - 5$$ . Based on the graph, which of the following describes the features of this function?

The function has a horizontal asymptote at y = -5 and decreases as x increases.

The function has a horizontal asymptote at y = 0 and increases as x increases.

The function has a vertical asymptote at x = -5 and increases as x increases.

The function has a horizontal asymptote at y = 5 and decreases as x increases.

Riley is analyzing the cooling rate of a special chemical, which follows the function f(x) = -2 log₂(-x - 8) + 5, where x represents the time in minutes after the reaction started. Riley wants to graph this function, including the asymptote and two points with integer coordinates. Which of the following is the correct graph for Riley's experiment?

A graph with a vertical asymptote at x = -8 and points (-9, 5) and (-10, 7) plotted.

A graph with a vertical asymptote at x = 8 and points (9, 5) and (10, 7) plotted.

A graph with a vertical asymptote at x = -2 and points (-3, 5) and (-4, 7) plotted.

A graph with a vertical asymptote at x = 2 and points (3, 5) and (4, 7) plotted.

Randy is analyzing the temperature drop in a science experiment, which follows the function f(x) = $$- (1/3)^{x+3} - 4$$ . He wants to know which of the following graphs correctly represents his data, including the asymptote and two points with integer coordinates. Which graph should Randy choose?

A graph with a horizontal asymptote at y = -4, passing through the points (-3, -5) and (-2, -5.33)

A graph with a horizontal asymptote at y = 0, passing through the points (0, 1) and (1, 2)

A graph with a horizontal asymptote at y = 4, passing through the points (3, 0) and (4, 1)

A graph with a horizontal asymptote at y = -4, passing through the points (0, -4.04) and (1, -4.13)

Sophia is analyzing the growth of three different investments. The value of the first investment grows proportionally to x, the second to y, and the third to z. She wants to fully expand the logarithm of the expression representing the combined growth: log (√y⁵z⁴/x⁵). Express the final answer in terms of log x, log y, and log z.

(5/2) log y + 4 log z − 5 log x

(5/2) log x + 4 log y − 5 log z

(5/2) log z + 4 log y − 5 log x

(5/2) log y + 4 log x − 5 log z

Henry is tracking the value of a car that depreciates over time. The value of the car after t months is given by the function f(t) = 820(0.86)^{t}. Write this function in the form f(t) = ab^{ $$\frac{t}{12}$$ }. Round all coefficients to four decimal places.

f(t) = 820 (0.1637)^{ $$\frac{t}{12}$$ }

f(t) = 820 (0.9130)^{ $$\frac{t}{12}$$ }

f(t) = 820 (0.8600)^{ $$\frac{t}{12}$$ }

f(t) = 820 (0.7200)^{ $$\frac{t}{12}$$ }

Riley invests $24,000 in an account that grows continuously at a rate of 24% per year. The amount in the account after t years is given by f(t) = $$24000e^{0.24t}$$ . Write this function in the form f(t) = a(2)^{t/k}. Round all coefficients to four decimal places.

f(t) = $$24000 (2^{1.2885})^{t}$$

f(t) = $$24000 (2^{0.2400})^{t}$$

f(t) = $$24000 (2^{0.6931})^{t}$$

f(t) = 24000 $$(2^{0.1200})^{t}$$

College Algebra Review Unit4 Exponential / Logarithmic Functions

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Mathematics

12th Grade

CCSS covered

College Algebra Review Unit4 Exponential / Logarithmic Functions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.HSF.LE.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.HSF.LE.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Riley invests $9,000 in a savings account with an annual interest rate of 8%. How much will be in Riley's account after 17 years, to the nearest cent?

33,300.16

21,500.00

18,000.50

25,000.75

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Sophia places $4,400 in a savings account with an annual interest rate of 8.25%. How much will be in Sophia's account after 29 years, to the nearest cent?

43,839.13

21,500.00

32,000.50

60,000.00

Tags

CCSS.HSF-LE.A.1C

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.HSF.LE.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.HSF.LE.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.HSA.APR.A.1

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College Algebra Review Unit4 Exponential / Logarithmic Functions

Riley invests $9,000 in a savings account with an annual interest rate of 8%. How much will be in Riley's account after 17 years, to the nearest cent?

Sophia places $4,400 in a savings account with an annual interest rate of 8.25%. How much will be in Sophia's account after 29 years, to the nearest cent?

Riley is working on a science project and needs to express the following fraction in its simplest form, using only positive exponents. Can you help Riley?

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