A relationship is shown. As the value of y decreases, what happens to the value of x?

The value of x increases and decreases.

Jill invests $400 in a savings bond. The value of the bond, V(t), in hundreds of dollars after x years is illustrated in the table below. Which equation and statement illustrate the approximate value of the bond in hundreds of dollars over time in years?

V(t) = 4(1.35)^x, and it grows.

V(t) = 4(0.65)^x, and it grows.

V(t) = 4(0.65)^x, and it decays.

V(t) = 4(1.35)^x, and it decays.

Which situation is not a linear function?

A $12,000 car depreciates 15% per year.

A gym charges a membership fee of $10.00 down and $10.00 per month.

A cab company charges $2.50 initially and $3.00 per mile.

A restaurant employee earns $12.50 per hour.

The function f is shown in the table below. Which type of function best models the given data?

C. linear function with positive rate of change

D. linear function with negative rate of change

Which table best represents an exponential relationship?

Table with x and y values: x | y 1 | 8 2 | 4 3 | 2 4 | 1 5 | 1/2

Table with x and y values: x | y 8 | 1 4 | 0 0 | 2 -4 | 3 -8 | 4

Table with x and y values: x | y 0 | 0 1 | 1 2 | 4 3 | 9 4 | 16

Table with x and y values: x | y 1 | 1 2 | 8 3 | 27 4 | 64 5 | 125

The table below shows the average yearly balance in a savings account where interest is compounded annually. No money is deposited or withdrawn after the initial amount is deposited. Which type of function best models the given data?

linear function with a negative rate of change

linear function with a positive rate of change

The equation V(t) = 12,000(0.75)^t represents the value of a motorcycle t years after it was purchased. Which statement is true?

The motorcycle cost $12,000 when purchased.

The motorcycle cost $9000 when purchased.

The motorcycle's value is decreasing at a rate of 75% each year.

The motorcycle's value is decreasing at a rate of 0.25% each year.

An equation to represent the value of a car after t months of ownership is v = 32,000(0.81)^t. Which statement is not correct?

The car maintained approximately 98% of its value each month.

The car lost approximately 1% of its value each month.

The value of the car when it was purchased was $32,000.

The value of the car 1 year after it was purchased was $25,920.

Some banks charge a fee on savings accounts that are left inactive for an extended period of time. The equation y = 5000(0.98)^x represents the value, y, of one account that was left inactive for a period of x years. What is the y-intercept of this equation and what does it represent?

5000, the amount of money in the account initially

0.98, the percent of money in the account initially

0.98, the percent of money in the account after x years

5000, the amount of money in the account after x years

Which statement is true about the graph of f(x) = (1/3)^x?

The graph is always decreasing.

The graph is always increasing.

The graph passes through (1, 0).

The graph has an asymptote, x = 0.

The Rickerts decided to set up an account for their daughter to pay for her college education. The day their daughter was born, they deposited $1000 in an account that pays 1.8% compounded annually. Beginning with her first birthday, they deposit an additional $750 into the account on each of her birthdays. Which expression correctly represents the amount of money in the account n years after their daughter was born?

a_0 = 1000 a_n = a_{n-1}(1.018) + 750

a_0 = 1000 a_n = a_{n-1}(1.018) + 750n

At her job, Pat earns $25,000 the first year and receives a raise of $1000 each year. The explicit formula for the nth term of this sequence is a_n = 25,000 + (n - 1)1000. Which rule best represents the equivalent recursive formula?

a_1 = 25,000, a_n = a_{n-1} + 1000

a_1 = 25,000, a_n = a_{n+1} + 1000

The average depreciation rate of a new boat is approximately 8% per year. If a new boat is purchased at a price of $75,000, which model is a recursive formula representing the value of the boat n years after it was purchased?

a_0 = 75,000, a_n = 0.92(a_{n-1})

Which graph represents a linear function of x?

Authored by Tanner Smith

Mathematics

9th Grade

CCSS covered

Used 3+ times

Which graph represents a linear function of x?

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which graph represents a linear function of x?

Diagram A

Diagram B

Diagram C

Diagram D

Which of the following is an example of a graph showing exponential growth?

Diagram A

Diagram B

Diagram C

Diagram D

The population of a type of bacteria triples every minute. The chart below represents the population of bacteria after t minutes. Which type of function represents the data?

linear

quadratic

exponential

absolute value

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Mr. Jenson gave his class the data below. As part of the class warm-up, Mr. Jenson asked his students to describe the shape of the graph created by these data points. Which of these student responses best describes the shape of the graph?

cubic

exponential

linear

quadratic

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The following exponential function describes the growth of a certain plant cell in t hours. p(t) = 3 · 16^t. How many plant cells are there after 3/4 hour?

A. 12

B. 18

C. 24

D. 36

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The population of a town is 345,000. The function f(t) = 345,000(1.2)^t gives the predicted population of the town in t years. Approximately what will the population be in 3 years?

A. 350,000

B. 600,000

C. 700,000

D. 1,250,000

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Alan won $2,000 in an essay contest. He invested the money in a savings account which pays 6% interest compounded annually. Consider the formula: A(t) = A0(1 + r)^t, where A(t) is the accumulated amount at time t, A0 is the amount invested at time t = 0, r is the interest rate, and t is time in years. What is Alan's investment worth after two years?

A. $240

B. $247

C. $2,240

D. $2,247

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Which graph represents a linear function of x?

Which graph represents a linear function of x?

Which of the following is an example of a graph showing exponential growth?

The population of a type of bacteria triples every minute. The chart below represents the population of bacteria after t minutes. Which type of function represents the data?

Mr. Jenson gave his class the data below. As part of the class warm-up, Mr. Jenson asked his students to describe the shape of the graph created by these data points. Which of these student responses best describes the shape of the graph?

The following exponential function describes the growth of a certain plant cell in t hours. p(t) = 3 · 16^t. How many plant cells are there after 3/4 hour?

The population of a town is 345,000. The function f(t) = 345,000(1.2)^t gives the predicted population of the town in t years. Approximately what will the population be in 3 years?

The value of Mr. Dulaney's car x years after its purchase is given by the function V(t) = 15,000(0.87)^t. Approximately, what was the value of Mr. Dulaney's car 5 years after its purchase?

Which pair of tables represent ( y_1 ) as a linear function and ( y_2 ) as an exponential function?

The value, ( V_{t+1} ), of a particular car is related to the previous year's value, ( V_t ), by the function ( V_{t+1} = (1 - 0.15)V_t ). Which statement best describes the change in the car's value from one year to the next?

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