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.