Question 1

Since life expectancy has increased in the last century, the number of Alzheimer's patients has increased dramatically. The number of patients in the United States reached 4 million in 2000. Using data collected since 2000, it has been found that the data can be modeled by the exponential function  where x is the years since 2000. Estimate the Alzheimer's patients in 2025. Round to the nearest tenth.

Accepted Answer

A)  8.0 million 
B)  3.9 million 
C)  4.8 million 
D)  7.8 million

Question 2

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y:
-xy = -5
A) A function with domain all real numbers except x = 0
B) Not a function; for example, when x = -5, y = ±1

Accepted Answer

The answer of Determine if the equation specifies a function...

Question 3

Find the vertex and the maximum or minimum of the quadratic function  by first writing f in standard form. State the range of f and find the intercepts of f .

Accepted Answer

The answer of Find the vertex and the maximum or...

Question 4

Graph the function.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 5

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y: -x² + y² = 36 A) A function with domain ℛ B) Not a function; for example, when x = 0, y = ±6

Accepted Answer

The answer of Determine if the equation specifies a function...

Question 6

If $4,000 is invested at 7% compounded annually, how long will it take for it to grow to $6,000, assuming no withdrawals are made? Compute answer to the next higher year if not exact.

Accepted Answer

A)  6 years 
B)  2 years 
C)  8 years 
D)  5 years

Question 7

For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical or horizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y = f(x).
-

Accepted Answer

A)   
B)   
C)   
D)

Question 8

In economics, functions that involve revenue, cost and profit are used. Suppose R(x) and C(x) denote the total revenue and the total cost, respectively, of producing a new high-tech widget. The difference  represents the total profit for producing x widgets. Given R(x) = 60x - 0.4  and  find the equation for P(x).

Accepted Answer

A)   
B)   
C)   
D)

Question 9

Use the properties of logarithms to solve:
-

Accepted Answer

A) 3 
B) 2 
C) 2,5 
D) 5

Question 10

Determine whether there is a maximum or minimum value for the given function, and find that value:
-

Accepted Answer

A)  Maximum: 10 
B)  Minimum: 4 
C)  Minimum: 0 
D)  Maximum: -4

Question 11

Solve the equation graphically to four decimal places:
-

Accepted Answer

A)  2.5000, 4.7500 
B)  2.5000 
C)  4.7500 
D)  No solution

Question 12

Find the function value:
-

Accepted Answer

A)   
B)   
C)   
D)

Question 13

Solve for x to two decimal places (using a calculator):
-

Accepted Answer

A)  1.07 
B)  5.17 
C)  2.32 
D)  22.97

Question 14

Convert to a logarithmic equation.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 15

Use a calculator to evaluate the expression. Round the result to five decimal places:
-ln 1097

Accepted Answer

A)  4.69775 
B)  3.04021 
C)  9.30292 
D)  7.00033

Question 16

Find the function value:
-Given that  , find f(t + 2).

Accepted Answer

A)   
B)   
C)  3t + 6 
D)

Question 17

A professional basketball player has a vertical leap of 37 inches. A formula relating an athlete's vertical leap V, in inches, to hang time T, in seconds, is V=  . What is his hang time? Round to the nearest tenth.

Accepted Answer

A)  1 sec 
B)  0.6 sec 
C)  0.9 sec 
D)  0.8 sec

Question 18

Use a calculator to evaluate the expression. Round the result to five decimal places:
-ln 0.027

Accepted Answer

A)  0.56864 
B)  -3.61192 
C)  -1.56864 
D)  Undefined

Question 19

The number of reports of a certain virus has increased exponentially since 1960. The current number of cases can be approximated using the function  where t is the number of years since 1960. Estimate the of cases in the year 2010.

Accepted Answer

A)  266 
B)  207 
C)  190 
D)  240

Question 20

Find the vertex form for the quadratic function. Then find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range
-

Accepted Answer

A)   
B)   
C)   
D)

Exam 2: Functions and Graphs

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y: -xy = -5 A) A function with domain all real numbers except x = 0 B) Not a function; for example, when x = -5, y = ±1

Find the vertex and the maximum or minimum of the quadratic function by first writing f in standard form. State the range of f and find the intercepts of f .

Graph the function. -

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y: -x² + y² = 36 A) A function with domain ℛ B) Not a function; for example, when x = 0, y = ±6

If $4,000 is invested at 7% compounded annually, how long will it take for it to grow to $6,000, assuming no withdrawals are made? Compute answer to the next higher year if not exact.

For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical or horizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y = f(x) . -

Use the properties of logarithms to solve: -

Determine whether there is a maximum or minimum value for the given function, and find that value: -

Solve the equation graphically to four decimal places: -

Find the function value: -

Solve for x to two decimal places (using a calculator) : -

Convert to a logarithmic equation. -

Use a calculator to evaluate the expression. Round the result to five decimal places: -ln 1097

Find the function value: -Given that , find f(t + 2) .

A professional basketball player has a vertical leap of 37 inches. A formula relating an athlete's vertical leap V, in inches, to hang time T, in seconds, is V= . What is his hang time? Round to the nearest tenth.

Use a calculator to evaluate the expression. Round the result to five decimal places: -ln 0.027

The number of reports of a certain virus has increased exponentially since 1960. The current number of cases can be approximated using the function where t is the number of years since 1960. Estimate the of cases in the year 2010.

Find the vertex form for the quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range -

Exam 2: Functions and Graphs

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y: -xy = -5 A) A function with domain all real numbers except x = 0 B) Not a function; for example, when x = -5, y = ±1

Find the vertex and the maximum or minimum of the quadratic function by first writing f in standard form. State the range of f and find the intercepts of f .

Graph the function. -

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y: -x2 + y2 = 36 A) A function with domain ℛ B) Not a function; for example, when x = 0, y = ±6

If $4,000 is invested at 7% compounded annually, how long will it take for it to grow to $6,000, assuming no withdrawals are made? Compute answer to the next higher year if not exact.

For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical or horizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y = f(x) . -

Use the properties of logarithms to solve: -

Determine whether there is a maximum or minimum value for the given function, and find that value: -

Solve the equation graphically to four decimal places: -

Find the function value: -

Solve for x to two decimal places (using a calculator) : -

Convert to a logarithmic equation. -

Use a calculator to evaluate the expression. Round the result to five decimal places: -ln 1097

Find the function value: -Given that , find f(t + 2) .

A professional basketball player has a vertical leap of 37 inches. A formula relating an athlete's vertical leap V, in inches, to hang time T, in seconds, is V= . What is his hang time? Round to the nearest tenth.

Use a calculator to evaluate the expression. Round the result to five decimal places: -ln 0.027

The number of reports of a certain virus has increased exponentially since 1960. The current number of cases can be approximated using the function where t is the number of years since 1960. Estimate the of cases in the year 2010.

Find the vertex form for the quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range -

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y: -x² + y² = 36 A) A function with domain ℛ B) Not a function; for example, when x = 0, y = ±6