Question 1

In 1996, the population of a country was estimated at 4 million. For any subsequent year the population  in millions is  where t is the number of years since 1996. Use a graphing calculator to estimate the population in 2005.
A) 4,743,000
B) 4,699,000
C) 4,655,000
D) 4,833,000

Accepted Answer

The answer of In 1996, the population of a country...

Question 2

Rewrite the following pair of functions as one composite function.  ; 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Rewrite the following pair of functions as...

Question 3

Indicate whether the function is an increasing or decreasing logistic function and identify the upper limiting value of the function  .
A) The function is decreasing and the upper limit is 29.00.
B) The function is decreasing and the upper limit is 2.37.
C) The function is decreasing and the upper limit is -2.37.
D) The function is increasing and the upper limit is 0.00.
E) The function is increasing and the upper limit is 29.00.

Accepted Answer

The answer of Indicate whether the function is an increasing...

Question 4

The total cost for producing  units of a commodity is $4.8 million, and the revenue generated by the sale of  units is $7.4 million. What is the profit on  units of the commodity?
A) $12.2 million
B) $1.5 million
C) $2.6 million
D) $4.8 million
E) $7.4 million

Accepted Answer

Profit = Revenue - Cost 
Profit on 11eaa894_64bf_0e2c_a158_b3cc77ddf5c3_TB6775_11 units = $7.4 million - $4.8 million 
Profit on 11eaa894_64bf_0e2c_a158_b3cc77ddf5c3_TB6775_11 units = $2.6 million

Therefore, the answer is (C) $2.6 million.

Question 5

Your credit card statement indicates a finance charge of 20.00 % per month on the outstanding balance. What is the effective rate of interest (APY) to the nearest hundredth?
A) 20.00 %
B) 21.94 %
C) 21.67 %
D) 240.00 %
E) 1.67 %

Accepted Answer

The effective annual rate (EAR) or annual percentage yield (APY) can be calculated using the formula for compound interest: $EAR = (1 + \frac{i}{n})^{n} - 1$, where $i$ is the nominal interest rate (in this case, 20% or 0.20 per month), and $n$ is the number of compounding periods per year (in this case, 12 months). Plugging the values into the formula gives $EAR = (1 + \frac{0.20}{12})^{12} - 1$, which approximately equals 0.2194 or 21.94% when converted to a percentage.

Question 6

The table gives the percent of the population of a certain city that was foreign born in the given year. Find a cubic function that best fits the data where x is the number of years after 1900 and y is equal to the percent. By trial and error, estimate the year the model predicts that the foreign-born population will be 100%. 
A)  foreign born population will be 100% in 1965.
B)  foreign born population will be 100% in 1975.
C)  foreign born population will be 100% in 1975.
D)  foreign born population will be 100% in 1965.
E)  foreign born population will be 100% in 1985.

Accepted Answer

The answer of The table gives the percent of the...

Question 7

Indicate whether the function is an increasing or decreasing logistic function and identify the upper limiting value of the function  .
A) The function is decreasing and the upper limit is 2.7.
B) The function is decreasing and the upper limit is -0.4.
C) The function is decreasing and the upper limit is 0.4.
D) The function is increasing and the upper limit is 4.2.
E) The function is increasing and the upper limit is 0.0.

Accepted Answer

The answer of Indicate whether the function is an increasing...

Question 8

Choose the function type for the mathematical model that best represents the given data set. 
A) logistic
B) quadratic
C) linear
D) exponential
E) logarithmic

Accepted Answer

The answer of Choose the function type for the mathematical...

Question 9

Calculate the total amount due after two years on a loan of $1100 with a simple interest charge of 7%.
A) $1254
B) $1204
C) $1304
D) $1354
E) $1154

Accepted Answer

The total amount due can be calculated using the formula for simple interest: Total Amount = Principal + (Principal * Rate * Time). Here, Principal = $1100, Rate = 7% or 0.07, and Time = 2 years. So, Total Amount = $1100 + ($1100 * 0.07 * 2) = $1100 + $154 = $1254.

Question 10

In 1990, there were 2 women among the CEOs of Fortune 500 companies. In 2009, this number had risen to 18 women. What was the percentage change in the number of Fortune 500 women CEOs between 1990 and 2009?
A) 800%
B) 8%
C) 180%
D) 20%
E) 91%

Accepted Answer

The percentage change is calculated by the formula: [(New Number - Original Number) / Original Number] * 100. So, [(18 - 2) / 2] * 100 = 800%.

Question 11

The following table gives the percent of the U.S. population with Internet connections for the years 1997 to 2003. Use a calculator to find the logistic function that models these data. Use x as the number of years past 1995.  Source: U.S. Department of Commerce
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The following table gives the percent of...

Question 12

Indicate whether the function is an increasing or decreasing logistic function and identify the upper limiting value of the function 
A) The function is increasing and the upper limit is 18.00.
B) The function is decreasing and the upper limit is 18.00.
C) The function is increasing and the upper limit is 68.00.
D) The function is decreasing and the upper limit is 68.00.
E) The function is decreasing and the upper limit is 0.00.

Accepted Answer

The answer of Indicate whether the function is an increasing...

Question 13

To offset college expenses, at the beginning of your freshman year you obtain a nonsubsidized student loan for $18,000. Interest on this loan accrues at a rate of 3.15% compounded monthly. However, you do not have to make any payments against either the principal or the interest until after you graduate. Write a model giving the total amount you will owe on this loan after t years in college.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of To offset college expenses, at the beginning...

Question 14

Find the equation of the quadratic function that is the best fit for the given data. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the equation of the quadratic function...

Question 15

A chemical reaction begins when a certain mixture reaches  C. The reaction activity is measured in units (U) per 100 microliters  of the mixture. Measurements during the first 18 minutes after the mixture reaches  C are listed in the accompanying table. Estimate the limiting value. 
A) 3.86
B) 1.93
C) 4.06
D) 3.83
E) 1.73

Accepted Answer

The answer of A chemical reaction begins when a certain...

Question 16

Rewrite the following pair of functions as one composite function.  ; 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Rewrite the following pair of functions as...

Question 17

Write the product of the two functions. Evaluate the constructed function at 2. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Write the product of the two functions....

Question 18

How long would it take an investment to double if the interest rate is 4.2%, compounded monthly? Round your answer to two decimal places.
A) 16.85 years
B) 0.48 year
C) 17.68 years
D) 16.53 years
E) 1.38 years

Accepted Answer

The answer of How long would it take an investment...

Question 19

What is the period of the following function? 
A) 14
B) 56
C) 2
D) 9
E) 11

Accepted Answer

The answer of What is the period of the following...

Question 20

It cost a company $6.75 to produce 75 glass bottles. What was the average cost of production of a glass bottle to the nearest cent?
A) $0.07
B) $0.75
C) $0.14
D) $40.88
E) $0.09

Accepted Answer

To find the average cost of production per glass bottle, divide the total cost by the number of bottles: $6.75 / 75 = $0.09.

Quiz 1: Ingredients of Change: Functions an Limits

In 1996, the population of a country was estimated at 4 million. For any subsequent year the population in millions is where t is the number of years since 1996. Use a graphing calculator to estimate the population in 2005.

Rewrite the following pair of functions as one composite function. ;

Indicate whether the function is an increasing or decreasing logistic function and identify the upper limiting value of the function .

The total cost for producing units of a commodity is $4.8 million, and the revenue generated by the sale of units is $7.4 million. What is the profit on units of the commodity?

Your credit card statement indicates a finance charge of 20.00 % per month on the outstanding balance. What is the effective rate of interest (APY) to the nearest hundredth?

Indicate whether the function is an increasing or decreasing logistic function and identify the upper limiting value of the function .

Choose the function type for the mathematical model that best represents the given data set.

Calculate the total amount due after two years on a loan of $1100 with a simple interest charge of 7%.

In 1990, there were 2 women among the CEOs of Fortune 500 companies. In 2009, this number had risen to 18 women. What was the percentage change in the number of Fortune 500 women CEOs between 1990 and 2009?

The following table gives the percent of the U.S. population with Internet connections for the years 1997 to 2003. Use a calculator to find the logistic function that models these data. Use x as the number of years past 1995. Source: U.S. Department of Commerce

Indicate whether the function is an increasing or decreasing logistic function and identify the upper limiting value of the function

Find the equation of the quadratic function that is the best fit for the given data.

A chemical reaction begins when a certain mixture reaches C. The reaction activity is measured in units (U) per 100 microliters of the mixture. Measurements during the first 18 minutes after the mixture reaches C are listed in the accompanying table. Estimate the limiting value.

Rewrite the following pair of functions as one composite function. ;

Write the product of the two functions. Evaluate the constructed function at 2.

How long would it take an investment to double if the interest rate is 4.2%, compounded monthly? Round your answer to two decimal places.

What is the period of the following function?

It cost a company $6.75 to produce 75 glass bottles. What was the average cost of production of a glass bottle to the nearest cent?