Question
11 - think about "plugging and chugging" from last week!
*
1 point
11. Five points from a function, f, are plotted in the first quadrant of the
coordinate plane, as shown.
y
0.2
0.175+
0.15
0.125
0.1 +
0.075 +
0.05
0.025 -
+X
0 0.5 1 1.5 2 2.5 3 3.5 4
Which equation could represent the function?
f (x) = 0.2(1-0.1)×
B
f (x) = 0.2(1-0.5)*
f (x) = 0.1(1-0.05)*
D f(x) = 0.1(1-0.25)*
A
B
C
D
19
*
1 point
19. Which equation models exponential growth?
1
1×
y = 2
5
@ y = 2(5.0)*
1×
y = 2 1 - 1*
5
D y = 2(1 - 0.5)*
A
B
C
D
20
*
1 point
20. Which function decays exponentially?
f(x) = = x
5
@ g(x) = 5x
@ h(x) = 5*
1
j(x) =
(는)
A
B
C
D
*
1 point
11. Five points from a function, f, are plotted in the first quadrant of the
coordinate plane, as shown.
y
0.2
0.175+
0.15
0.125
0.1 +
0.075 +
0.05
0.025 -
+X
0 0.5 1 1.5 2 2.5 3 3.5 4
Which equation could represent the function?
f (x) = 0.2(1-0.1)×
B
f (x) = 0.2(1-0.5)*
f (x) = 0.1(1-0.05)*
D f(x) = 0.1(1-0.25)*
A
B
C
D
19
*
1 point
19. Which equation models exponential growth?
1
1×
y = 2
5
@ y = 2(5.0)*
1×
y = 2 1 - 1*
5
D y = 2(1 - 0.5)*
A
B
C
D
20
*
1 point
20. Which function decays exponentially?
f(x) = = x
5
@ g(x) = 5x
@ h(x) = 5*
1
j(x) =
(는)
A
B
C
D
Answers
GPT-4o mini
Let's analyze the questions step-by-step.
**Question 11: Identifying the Function Based on Coordinates**
You have several function options, and you need to decide which one best fits the points plotted in the first quadrant. Unfortunately, we don't have the actual points plotted, but here's how to approach it if you had the graph:
1. Look for a trend: Check if the points seem to suggest linear growth, exponential growth, or decay.
2. Compare your options.
- A: \( f(x) = 0.2(1 - 0.1)^x \)
- B: \( f(x) = 0.2(1 - 0.5)^x \)
- C: \( f(x) = 0.1(1 - 0.05)^x \)
- D: \( f(x) = 0.1(1 - 0.25)^x \)
If the y-values are increasing, options that show an increase (like options A and C) might be valid. If they are decreasing (but not constantly), we would lean towards options that imply decay. You would select based on the trend of the plotted points.
**Question 19: Which Equation Models Exponential Growth?**
The goal is to identify exponential growth models:
1. \( y = 2 \)
2. \( y = 2(5^x) \)
3. \( y = 2(1 - 1/5)^x \)
4. \( y = 2(1 - 0.5)^x \)
From these options:
- The second equation, \( y = 2(5^x) \), represents exponential growth, as it employs a base greater than one being raised to a power (the variable \(x\)).
**Answer: B \( y = 2(5^x) \)**
**Question 20: Which Function Decays Exponentially?**
You want to determine which option shows exponential decay:
1. \( f(x) = x^5 \) (Polynomial function)
2. \( g(x) = 5^x \) (Exponential growth because the base is > 1)
3. \( h(x) = 5 \cdot (1/5)^x \) (Exponential decay because it involves a fraction base < 1 raised to a positive x)
4. \( j(x) = \text{{(unknown function)}} \) (Hard to determine without the function provided)
Exponential decay occurs when you have a base between 0 and 1 raised to a variable.
**Answer: C \( h(x) = 5 \cdot (1/5)^x \)**
To summarize:
- **Question 11:** Select based on your plotted points.
- **Question 19:** B \( y = 2(5^x) \)
- **Question 20:** C \( h(x) = 5 \cdot (1/5)^x \)
If you have further details on the points for Question 11 or additional context, please provide them for a more accurate answer!
**Question 11: Identifying the Function Based on Coordinates**
You have several function options, and you need to decide which one best fits the points plotted in the first quadrant. Unfortunately, we don't have the actual points plotted, but here's how to approach it if you had the graph:
1. Look for a trend: Check if the points seem to suggest linear growth, exponential growth, or decay.
2. Compare your options.
- A: \( f(x) = 0.2(1 - 0.1)^x \)
- B: \( f(x) = 0.2(1 - 0.5)^x \)
- C: \( f(x) = 0.1(1 - 0.05)^x \)
- D: \( f(x) = 0.1(1 - 0.25)^x \)
If the y-values are increasing, options that show an increase (like options A and C) might be valid. If they are decreasing (but not constantly), we would lean towards options that imply decay. You would select based on the trend of the plotted points.
**Question 19: Which Equation Models Exponential Growth?**
The goal is to identify exponential growth models:
1. \( y = 2 \)
2. \( y = 2(5^x) \)
3. \( y = 2(1 - 1/5)^x \)
4. \( y = 2(1 - 0.5)^x \)
From these options:
- The second equation, \( y = 2(5^x) \), represents exponential growth, as it employs a base greater than one being raised to a power (the variable \(x\)).
**Answer: B \( y = 2(5^x) \)**
**Question 20: Which Function Decays Exponentially?**
You want to determine which option shows exponential decay:
1. \( f(x) = x^5 \) (Polynomial function)
2. \( g(x) = 5^x \) (Exponential growth because the base is > 1)
3. \( h(x) = 5 \cdot (1/5)^x \) (Exponential decay because it involves a fraction base < 1 raised to a positive x)
4. \( j(x) = \text{{(unknown function)}} \) (Hard to determine without the function provided)
Exponential decay occurs when you have a base between 0 and 1 raised to a variable.
**Answer: C \( h(x) = 5 \cdot (1/5)^x \)**
To summarize:
- **Question 11:** Select based on your plotted points.
- **Question 19:** B \( y = 2(5^x) \)
- **Question 20:** C \( h(x) = 5 \cdot (1/5)^x \)
If you have further details on the points for Question 11 or additional context, please provide them for a more accurate answer!