Question
Given f, of, x, equals, 3, x, plus, 3f(x)=3x+3, solve for xx when f, of, x, equals, 6f(x)=6.
Answers
Answer
Given f, of, x, equals, minus, 3, x, minus, 2f(x)=−3x−2, find f, of, 2f(2).
Answer
that was rong
Answer
22 isnt the right answer
Answer
A town has a population of 2, point, 3, 5, times, 10, to the power 42.35×10
4
and shrinks at a rate of 9.1% every year. Which equation represents the town’s population after 2 years?
Answer
Multiple Choice Answers
P, equals, left parenthesis, 2, point, 3, 5, times, 10, to the power 4 , right parenthesis, left parenthesis, 1, plus, 0, point, 0, 9, 1, right parenthesis, squaredP=(2.35×10
4
)(1+0.091)
2
P, equals, left parenthesis, 2, point, 3, 5, times, 10, to the power 4 , right parenthesis, left parenthesis, 0, point, 0, 9, right parenthesis, squaredP=(2.35×10
4
)(0.09)
2
P, equals, left parenthesis, 2, point, 3, 5, times, 10, to the power 4 , right parenthesis, left parenthesis, 1, minus, 0, point, 0, 9, 1, right parenthesis, left parenthesis, 1, minus, 0, point, 0, 9, 1, right parenthesis, left parenthesis, 1, minus, 0, point, 0, 9, 1, right parenthesis, left parenthesis, 1, minus, 0, point, 0, 9, 1, right parenthesisP=(2.35×10
4
)(1−0.091)(1−0.091)(1−0.091)(1−0.091)
P, equals, left parenthesis, 2, point, 3, 5, times, 10, to the power 4 , right parenthesis, left parenthesis, 0, point, 9, 0, 9, right parenthesis, squaredP=(2.35×10
4
)(0.909)
2
4
and shrinks at a rate of 9.1% every year. Which equation represents the town’s population after 2 years?
Answer
Multiple Choice Answers
P, equals, left parenthesis, 2, point, 3, 5, times, 10, to the power 4 , right parenthesis, left parenthesis, 1, plus, 0, point, 0, 9, 1, right parenthesis, squaredP=(2.35×10
4
)(1+0.091)
2
P, equals, left parenthesis, 2, point, 3, 5, times, 10, to the power 4 , right parenthesis, left parenthesis, 0, point, 0, 9, right parenthesis, squaredP=(2.35×10
4
)(0.09)
2
P, equals, left parenthesis, 2, point, 3, 5, times, 10, to the power 4 , right parenthesis, left parenthesis, 1, minus, 0, point, 0, 9, 1, right parenthesis, left parenthesis, 1, minus, 0, point, 0, 9, 1, right parenthesis, left parenthesis, 1, minus, 0, point, 0, 9, 1, right parenthesis, left parenthesis, 1, minus, 0, point, 0, 9, 1, right parenthesisP=(2.35×10
4
)(1−0.091)(1−0.091)(1−0.091)(1−0.091)
P, equals, left parenthesis, 2, point, 3, 5, times, 10, to the power 4 , right parenthesis, left parenthesis, 0, point, 9, 0, 9, right parenthesis, squaredP=(2.35×10
4
)(0.909)
2
Answer
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y, equals, 38, left parenthesis, 1, point, 0, 9, right parenthesis, to the power x
y=38(1.09)
x
Answer
Growth
% increase Submit Answer
y, equals, 38, left parenthesis, 1, point, 0, 9, right parenthesis, to the power x
y=38(1.09)
x
Answer
Growth
% increase Submit Answer
Answered by
GPT-4o mini
We are given the function \( f(x) = 3x + 3 \). We need to find \( x \) when \( f(x) = 6 \).
1. Start by setting the equation for \( f(x) \):
\[
f(x) = 3x + 3
\]
2. Set \( f(x) \) equal to \( 6 \):
\[
3x + 3 = 6
\]
3. Subtract \( 3 \) from both sides:
\[
3x = 6 - 3
\]
\[
3x = 3
\]
4. Divide both sides by \( 3 \):
\[
x = 1
\]
Thus, the solution for \( x \) when \( f(x) = 6 \) is \( \boxed{1} \).
1. Start by setting the equation for \( f(x) \):
\[
f(x) = 3x + 3
\]
2. Set \( f(x) \) equal to \( 6 \):
\[
3x + 3 = 6
\]
3. Subtract \( 3 \) from both sides:
\[
3x = 6 - 3
\]
\[
3x = 3
\]
4. Divide both sides by \( 3 \):
\[
x = 1
\]
Thus, the solution for \( x \) when \( f(x) = 6 \) is \( \boxed{1} \).
Answered by
GPT-4o mini
We are given the function \( f(x) = -3x - 2 \). We need to find \( f(2) \) and then evaluate \( f(f(2)) \).
1. **Calculate \( f(2) \)**:
\[
f(2) = -3(2) - 2
\]
\[
= -6 - 2
\]
\[
= -8
\]
2. **Now calculate \( f(f(2)) = f(-8) \)**:
\[
f(-8) = -3(-8) - 2
\]
\[
= 24 - 2
\]
\[
= 22
\]
So, \( f(f(2)) = f(-8) = 22 \).
Thus, the final answer is \( \boxed{22} \).
1. **Calculate \( f(2) \)**:
\[
f(2) = -3(2) - 2
\]
\[
= -6 - 2
\]
\[
= -8
\]
2. **Now calculate \( f(f(2)) = f(-8) \)**:
\[
f(-8) = -3(-8) - 2
\]
\[
= 24 - 2
\]
\[
= 22
\]
So, \( f(f(2)) = f(-8) = 22 \).
Thus, the final answer is \( \boxed{22} \).
Answered by
GPT-4o mini
Let's go through the problem again step by step.
We have the function defined as:
\[
f(x) = -3x - 2
\]
We need to find \( f(2) \) and then evaluate \( f(f(2)) \).
1. **Calculate \( f(2) \)**:
\[
f(2) = -3(2) - 2
\]
\[
= -6 - 2
\]
\[
= -8
\]
2. **Now calculate \( f(f(2)) = f(-8) \)**:
\[
f(-8) = -3(-8) - 2
\]
\[
= 24 - 2
\]
\[
= 22
\]
Thus, after reviewing the calculations, the result is indeed correct.
So, \( f(f(2)) = f(-8) = 22 \).
Final answer: \( \boxed{22} \).
If there’s a specific part that you believe is incorrect or if there is additional context to consider, please let me know!
We have the function defined as:
\[
f(x) = -3x - 2
\]
We need to find \( f(2) \) and then evaluate \( f(f(2)) \).
1. **Calculate \( f(2) \)**:
\[
f(2) = -3(2) - 2
\]
\[
= -6 - 2
\]
\[
= -8
\]
2. **Now calculate \( f(f(2)) = f(-8) \)**:
\[
f(-8) = -3(-8) - 2
\]
\[
= 24 - 2
\]
\[
= 22
\]
Thus, after reviewing the calculations, the result is indeed correct.
So, \( f(f(2)) = f(-8) = 22 \).
Final answer: \( \boxed{22} \).
If there’s a specific part that you believe is incorrect or if there is additional context to consider, please let me know!
Answered by
GPT-4o mini
Let's go through the calculations again step by step to ensure accuracy.
Given the function \( f(x) = -3x - 2 \), we want to find \( f(2) \) first, and then use that result to find \( f(f(2)) \).
### Step 1: Calculate \( f(2) \)
\[
f(2) = -3(2) - 2
\]
Calculating this step by step:
\[
= -6 - 2
\]
\[
= -8
\]
So, \( f(2) = -8 \).
### Step 2: Calculate \( f(f(2)) = f(-8) \)
Now we will find \( f(-8) \):
\[
f(-8) = -3(-8) - 2
\]
Calculating this step by step:
\[
= 24 - 2
\]
\[
= 22
\]
### Conclusion
After double-checking, the calculations and results show:
- \( f(2) = -8 \)
- \( f(f(2)) = f(-8) = 22 \)
If you have a different interpretation of the question or if there are additional details, please share them, and I'll be happy to assist further! Based on the calculations provided, \( \boxed{22} \) is indeed the result for \( f(f(2)) \).
Given the function \( f(x) = -3x - 2 \), we want to find \( f(2) \) first, and then use that result to find \( f(f(2)) \).
### Step 1: Calculate \( f(2) \)
\[
f(2) = -3(2) - 2
\]
Calculating this step by step:
\[
= -6 - 2
\]
\[
= -8
\]
So, \( f(2) = -8 \).
### Step 2: Calculate \( f(f(2)) = f(-8) \)
Now we will find \( f(-8) \):
\[
f(-8) = -3(-8) - 2
\]
Calculating this step by step:
\[
= 24 - 2
\]
\[
= 22
\]
### Conclusion
After double-checking, the calculations and results show:
- \( f(2) = -8 \)
- \( f(f(2)) = f(-8) = 22 \)
If you have a different interpretation of the question or if there are additional details, please share them, and I'll be happy to assist further! Based on the calculations provided, \( \boxed{22} \) is indeed the result for \( f(f(2)) \).
Answered by
GPT-4o mini
To find the correct equation representing the town's population after 2 years given an initial population and a yearly decline, we start with the information provided:
### Given:
- Initial population \( P_0 = 2.35 \times 10^4 \)
- Decline rate = 9.1% per year
### Process:
1. The decline will lead to a multiplier for the population each year. Since the town is shrinking at a rate of 9.1% per year, the population after 1 year will be:
\[
P_1 = P_0 \times (1 - 0.091) = P_0 \times 0.909
\]
2. After 2 years, the population will decline again by the same rate:
\[
P_2 = P_1 \times (1 - 0.091) = P_0 \times 0.909 \times 0.909 = P_0 \times (0.909)^2
\]
Thus, the population after 2 years can be expressed as:
\[
P = P_0 \times (0.909)^2
\]
### Compare with Answer Choices
Considering the choices you provided, the correct equation is:
\[
P = (2.35 \times 10^4)(0.909)^2
\]
So the answer is:
\[
P = (2.35 \times 10^4)(0.909)^2
\]
### Conclusion
Therefore, the correct option from the given choices is:
**\(P = (2.35 \times 10^4)(0.909)^2\)**.
### Given:
- Initial population \( P_0 = 2.35 \times 10^4 \)
- Decline rate = 9.1% per year
### Process:
1. The decline will lead to a multiplier for the population each year. Since the town is shrinking at a rate of 9.1% per year, the population after 1 year will be:
\[
P_1 = P_0 \times (1 - 0.091) = P_0 \times 0.909
\]
2. After 2 years, the population will decline again by the same rate:
\[
P_2 = P_1 \times (1 - 0.091) = P_0 \times 0.909 \times 0.909 = P_0 \times (0.909)^2
\]
Thus, the population after 2 years can be expressed as:
\[
P = P_0 \times (0.909)^2
\]
### Compare with Answer Choices
Considering the choices you provided, the correct equation is:
\[
P = (2.35 \times 10^4)(0.909)^2
\]
So the answer is:
\[
P = (2.35 \times 10^4)(0.909)^2
\]
### Conclusion
Therefore, the correct option from the given choices is:
**\(P = (2.35 \times 10^4)(0.909)^2\)**.
Answered by
GPT-4o mini
The given exponential function is:
\[
y = 38(1.09)^x
\]
### Identifying Growth or Decay
In the function, the base of the exponent is \(1.09\). Since this base is greater than 1, the function represents **growth**.
### Determining the Percentage Rate of Increase
The percentage growth rate can be derived as follows:
1. **Base of the exponent**: The \(1.09\) indicates that for each unit increase in \(x\), \(y\) is multiplied by \(1.09\).
2. **Percentage increase**: To find the percentage increase, we subtract 1 from the base and convert it to a percentage:
\[
\text{Percentage increase} = (1.09 - 1) \times 100\% = 0.09 \times 100\% = 9\%
\]
### Final Answer
Thus, the function represents **growth**, and the percentage rate of increase is:
**Growth**
**9% increase**
\[
y = 38(1.09)^x
\]
### Identifying Growth or Decay
In the function, the base of the exponent is \(1.09\). Since this base is greater than 1, the function represents **growth**.
### Determining the Percentage Rate of Increase
The percentage growth rate can be derived as follows:
1. **Base of the exponent**: The \(1.09\) indicates that for each unit increase in \(x\), \(y\) is multiplied by \(1.09\).
2. **Percentage increase**: To find the percentage increase, we subtract 1 from the base and convert it to a percentage:
\[
\text{Percentage increase} = (1.09 - 1) \times 100\% = 0.09 \times 100\% = 9\%
\]
### Final Answer
Thus, the function represents **growth**, and the percentage rate of increase is:
**Growth**
**9% increase**
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