An expression is shown below:

Question

square root of 32 plus square root of 2

Which statement is true about the expression?

It is rational and equal to 4.
It is rational and equal to 5.
It is irrational and equal to 5 multiplied by square root of 2.
It is irrational and equal to 4 multiplied by square root of 2.
Question 2(Multiple Choice Worth 4 points)

(03.02 MC)

Finbar bought his home for $150,000 in 2010. Property values have increased 10% every year since he has owned the home. Which of the following equations can be used to represent the price of the home x years after 2010?

y = 150,000(1.5)x
y = 150,000(1.1)x
y = 150,000(0.9)x
y = 150,000(0.5)x
Question 3(Multiple Choice Worth 4 points)

(03.02 LC)

Which of the following is a function equivalent to f(x) = 4(1.8)2x?

f(x) = 4(3.24)x
f(x) = 4(3.24x)
f(x) = 12.96x
f(x) = 51.84x
Question 4(Multiple Choice Worth 4 points)

(03.05 MC)

The functions f(x) and g(x) in the table below show Jane's and Mariah's savings respectively, in dollars, after x years. Some values are missing in the table.

x(years) 1 2 3
f(x) = 2x
Jane's savings in dollars 2 4
g(x) = 2x
Mariah's savings in dollars 2 4

Which statement best describes Jane's and Mariah's savings in the long run?
Jane will save more than Mariah.
Mariah will save more than Jane.
The savings will increase by the same factor for both.
The savings will increase by the same percentage for both.
Question 5(Multiple Choice Worth 4 points)

(03.04 MC)

Graph the function f(x) = 16(1.87)x. Does this function show growth or decay? What is the equation of the asymptote?

Growth; y = −16
Growth; y = 0
Decay; y = −16
Decay; y = 0
Question 6(Multiple Choice Worth 4 points)

(03.05 MC)

The same amount of trash is dumped into a landfill every day. The function below shows the total number of tons of trash n in the landfill after x days:

n = 2000x + 1000

What does the number 1,000 represent?

Amount of trash originally in the landfill
Amount of trash added to the landfill every day
Rate at which the total trash increases every day
Rate at which the new trash increases every day
Question 7(Multiple Choice Worth 4 points)

(03.03 MC)

The population of a species of fish in a river increased by a factor of 1.05 every day for the amount of days shown in the graph. The function shows the number of fish in the river f(x) after x days:

f(x) = 100(1.05)x

exponential graph showing Time in Days on the x axis and Number of Fish on the y axis going through zero comma one hundred and approximately thirty one comma four hundred fifty four

Which of the following is a reasonable domain for the function days 0 to 31?

0 ≤ x ≤ 100
0 ≤ x ≤ 31
All positive integers greater than 100
All positive integers less than 100
Question 8(Multiple Choice Worth 4 points)

(03.01 LC)

Which of the following is equal to the square root of the cube root of 5?

5 to the power of one third
5 to the power of one sixth
5 to the power of two thirds
5 to the power of three halves
Question 9(Multiple Choice Worth 4 points)

(03.05 MC)

The table represents the amount of money in a bank account each month.

Month Balance ($)
1 2,215.25
2 2,089.75
3 1,964.25
4 1,838.75
5 1,713.25

What type of function represents the bank account as a function of time? Justify your answer.
This is an exponential function because there is a common difference in the balance between the months.
This is an exponential function because there is a common ratio in the balance between the months.
This is a linear function because there is a common difference in the balance between the months.
This is a linear function because there is a common ratio in the balance between the months.
Question 10(Multiple Choice Worth 4 points)

(03.04 LC)

Peter made custard every weekend. The more times he made custard, the more practice he gained. The time he took to make the same amount of custard every week decreased with practice. The function below shows the number of hours f(x) Peter took to make custard after he had made it x times:

f(x) = 2(0.6)x

Which graph best represents the function?

graph of an increasing exponential function going through six tenths on the y axis
graph of a decreasing exponential function going through one on the y axis
graph of a decreasing exponential function going through two on the y axis
graph of an increasing exponential function going through one on the y axis
Question 11(Multiple Choice Worth 4 points)

(03.04 MC)

Clara is taking a medicine for a common cold. The table below shows the amount of medicine f(t), in mg, that was present in Clara's body after time t:

t (hours) 1 2 3 4 5
f(t) (mg) 236.5 223.73 211.65 200.22 189.41

Heidi was administered 300 mg of the same medicine. The amount of medicine in her body f(t) after time t is shown by the equation below:

f(t) = 300(0.946)t

Which statement best describes the rate at which Clara's and Heidi's bodies eliminated the medicine?
Clara's body eliminated the antibiotic faster than Heidi's body.
Clara's body eliminated the antibiotic at the same rate as Heidi's body.
Clara's body eliminated the antibiotic at half of the rate at which Heidi's body eliminated the antibiotic.
Clara's body eliminated the antibiotic at one-fourth of the rate at which Heidi's body eliminated the antibiotic.
Question 12(Multiple Choice Worth 4 points)

(03.05 MC)

Graph h(x) = 38(0.51)x. What is the constant percent rate of change of f(x) with respect to x? Does the graph show growth or decay?

49% growth
49% decay
51% growth
51% decay
Question 13(Multiple Choice Worth 4 points)

(03.02 MC)

The function below represents the interest Jessi earns on an investment. Identify the term that represents the amount of money originally invested.

f(x) = 1,000(1 + 0.05)x

1,000
1
0.05
1.05
Question 14(Multiple Choice Worth 4 points)

(03.03 MC)

Diana invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of her investment after x years:

f(x) = 400(1.01)x

What was the average rate of change of the value of Diana's investment from the second year to the fifth year?

1.01 dollars per year
2.47 dollars per year
4.12 dollars per year
12.36 dollars per year
Question 15(Multiple Choice Worth 4 points)

(03.03 MC)

The following table shows the expressions that represent the sales of two companies:

Company A B
Sales 170(1.04)x 330(1.80)x

Which company has the largest percent of increase?
Both Company A and Company B
Neither Company A nor Company B
Company A
Company B

Answer 1

Here are the answers to each of the multiple-choice questions provided:

Question 1:

• True Statement about the Expression: It is irrational and equal to 4 multiplied by square root of 2.
  • Explanation: \( \sqrt{32} = 4\sqrt{2} \), so \( \sqrt{32} + \sqrt{2} = 4\sqrt{2} + \sqrt{2} = 5\sqrt{2} \), which is again irrational.

Question 2:

• Equation for Property Value Growth: \( y = 150,000(1.1)^x \)
  • Explanation: Since the property values increase by 10% every year, the growth factor is \( 1 + 0.10 = 1.1 \).

Question 3:

• Function Equivalent: \( f(x) = 4(3.24)^x \)
  • Explanation: \( 1.8^{2x} = (1.8^2)^x = (3.24)^x \).

Question 4:

• Statement about Savings: The savings will increase by the same factor for both.
  • Explanation: Both functions are linear with the same rate of increase.

Question 5:

• Function Behavior: Growth; \( y = 0 \)
  • Explanation: The base \( 1.87 > 1 \) shows growth, and the horizontal asymptote for exponential growth is \( y = 0 \).

Question 6:

• Interpretation of the Equation: Amount of trash originally in the landfill
  • Explanation: The equation shows \( 1,000 \) as the initial amount when \( x = 0 \).

Question 7:

• Reasonable Domain for Fish Population: \( 0 \leq x \leq 31 \)
  • Explanation: It represents the days from 0 to 31 as indicated in the graph.

Question 8:

• Equivalent Expression: \( 5 \) to the power of one sixth
  • Explanation: The cube root of \( 5 \) is \( 5^{1/3} \), and then taking the square root gives \( (5^{1/3})^{1/2} = 5^{1/6} \).

Question 9:

• Type of Function: This is a linear function because there is a common difference in the balance between the months.
  • Explanation: The balances decrease at a consistent rate.

Question 10:

• Graph Representation: Graph of a decreasing exponential function going through two on the y-axis.
  • Explanation: The function \( f(x) = 2(0.6)^x \) starts at \( 2 \) and decreases over time.

Question 11:

• Comparison of Elimination Rates: Clara's body eliminated the antibiotic at half of the rate at which Heidi's body eliminated the antibiotic.
  • Explanation: Calculating rates gives insight into the elimination from each of their bodies.

Question 12:

• Constant Percent Rate of Change: 51% decay
  • Explanation: The base \( 0.51 \) indicates decay, and the constant percent change is \( 1 - 0.51 = 0.49 \text{ or } 49% \).

Question 13:

• Term for Original Investment: \( 1,000 \)
  • Explanation: This is the principal amount invested originally.

Question 14:

• Average Rate of Change: 12.36 dollars per year
  • Explanation: Calculate the value at years 2 and 5 and find the change over the difference in years.

Question 15:

• Company with the Largest Percent Increase: Company B
  • Explanation: Company B has a larger growth factor (1.80) compared to Company A (1.04).

These answers encapsulate the reasoning and explanation behind each option in your questions.