Question
Given f, of, x, equals, 2, x, squared, plus, 7, x, plus, 18f(x)=2x
2
+7x+18, find f, of, minus, 4f(−4)
2
+7x+18, find f, of, minus, 4f(−4)
Answers
Answer
A town has a population of 17000 and grows at 4% every year. What will be the population after 5 years, to the nearest whole number?
Answer
thats rong
Answer
thats the same answer from earlier and i just told you it was rong i think somthing wasnt put in correctly
A town has a population of 17000 and grows at 4% every year. What will be the population after 5 years, to the nearest whole number?
A town has a population of 17000 and grows at 4% every year. What will be the population after 5 years, to the nearest whole number?
Answer
Casho's math teacher said that each question answered correctly on a test would be worth 3 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test.
Answer
Attempt 1 out of 3
The independent variable, x, represents the
, and the dependent variable is the
, because the
depends on the
.
A function relating these variables is Q, left parenthesis, x, right parenthesis, equalsQ(x)=
.
So Q, left parenthesis, 17, right parenthesis, equalsQ(17)=
, meaning 1717
Answer
Attempt 1 out of 3
The independent variable, x, represents the
, and the dependent variable is the
, because the
depends on the
.
A function relating these variables is Q, left parenthesis, x, right parenthesis, equalsQ(x)=
.
So Q, left parenthesis, 17, right parenthesis, equalsQ(17)=
, meaning 1717
Answered by
GPT-4o mini
To find \( f(-4) \) for the function \( f(x) = 2x^2 + 7x + 18 \), we will substitute \(-4\) into the function:
\[
f(-4) = 2(-4)^2 + 7(-4) + 18
\]
Now, calculate each term step by step:
1. Calculate \((-4)^2\):
\[
(-4)^2 = 16
\]
2. Now multiply by 2:
\[
2 \times 16 = 32
\]
3. Calculate \(7(-4)\):
\[
7 \times -4 = -28
\]
4. Now substitute these values into the expression:
\[
f(-4) = 32 - 28 + 18
\]
5. Combine the constants:
\[
32 - 28 = 4
\]
\[
4 + 18 = 22
\]
So, we find that:
\[
f(-4) = 22
\]
Thus, the final answer is:
\[
\boxed{22}
\]
\[
f(-4) = 2(-4)^2 + 7(-4) + 18
\]
Now, calculate each term step by step:
1. Calculate \((-4)^2\):
\[
(-4)^2 = 16
\]
2. Now multiply by 2:
\[
2 \times 16 = 32
\]
3. Calculate \(7(-4)\):
\[
7 \times -4 = -28
\]
4. Now substitute these values into the expression:
\[
f(-4) = 32 - 28 + 18
\]
5. Combine the constants:
\[
32 - 28 = 4
\]
\[
4 + 18 = 22
\]
So, we find that:
\[
f(-4) = 22
\]
Thus, the final answer is:
\[
\boxed{22}
\]
Answered by
GPT-4o mini
To calculate the population after 5 years given an initial population of 17,000 and an annual growth rate of 4%, we can use the formula for exponential growth:
\[
P(t) = P_0 \times (1 + r)^t
\]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal),
- \( t \) is the time in years.
Here, the values are:
- \( P_0 = 17000 \)
- \( r = 0.04 \)
- \( t = 5 \)
Now plug in the values:
\[
P(5) = 17000 \times (1 + 0.04)^5
\]
\[
P(5) = 17000 \times (1.04)^5
\]
Now, calculate \( (1.04)^5 \):
\[
(1.04)^5 \approx 1.216652902
\]
Now multiply by the initial population:
\[
P(5) \approx 17000 \times 1.216652902 \approx 20684.11535
\]
Rounding to the nearest whole number, the population after 5 years will be approximately:
\[
\boxed{20684}
\]
\[
P(t) = P_0 \times (1 + r)^t
\]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal),
- \( t \) is the time in years.
Here, the values are:
- \( P_0 = 17000 \)
- \( r = 0.04 \)
- \( t = 5 \)
Now plug in the values:
\[
P(5) = 17000 \times (1 + 0.04)^5
\]
\[
P(5) = 17000 \times (1.04)^5
\]
Now, calculate \( (1.04)^5 \):
\[
(1.04)^5 \approx 1.216652902
\]
Now multiply by the initial population:
\[
P(5) \approx 17000 \times 1.216652902 \approx 20684.11535
\]
Rounding to the nearest whole number, the population after 5 years will be approximately:
\[
\boxed{20684}
\]
Answered by
GPT-4o mini
I apologize for any confusion. Let's go through the calculations step by step again to ensure we calculate the population correctly after 5 years with a growth rate of 4%.
### Given:
- Initial population \( P_0 = 17000 \)
- Growth rate \( r = 4\% = 0.04 \)
- Time \( t = 5 \) years
### Formula:
The formula for population growth is:
\[
P(t) = P_0 \times (1 + r)^t
\]
### Calculation:
Substituting the values into the formula:
\[
P(5) = 17000 \times (1 + 0.04)^5
\]
\[
P(5) = 17000 \times (1.04)^5
\]
Now we need to calculate \( (1.04)^5 \):
\[
(1.04)^5 \approx 1.216652902
\]
Now, multiplying this by the initial population:
\[
P(5) \approx 17000 \times 1.216652902
\]
\[
P(5) \approx 20684.10934
\]
### Rounding:
Rounding this to the nearest whole number gives us:
\[
P(5) \approx 20684
\]
Upon re-evaluation of the calculations, it appears that the final population after 5 years, to the nearest whole number, is indeed:
\[
\boxed{20684}
\]
If there are specific aspects of the calculation you believe are incorrect or if there's additional context, please let me know!
### Given:
- Initial population \( P_0 = 17000 \)
- Growth rate \( r = 4\% = 0.04 \)
- Time \( t = 5 \) years
### Formula:
The formula for population growth is:
\[
P(t) = P_0 \times (1 + r)^t
\]
### Calculation:
Substituting the values into the formula:
\[
P(5) = 17000 \times (1 + 0.04)^5
\]
\[
P(5) = 17000 \times (1.04)^5
\]
Now we need to calculate \( (1.04)^5 \):
\[
(1.04)^5 \approx 1.216652902
\]
Now, multiplying this by the initial population:
\[
P(5) \approx 17000 \times 1.216652902
\]
\[
P(5) \approx 20684.10934
\]
### Rounding:
Rounding this to the nearest whole number gives us:
\[
P(5) \approx 20684
\]
Upon re-evaluation of the calculations, it appears that the final population after 5 years, to the nearest whole number, is indeed:
\[
\boxed{20684}
\]
If there are specific aspects of the calculation you believe are incorrect or if there's additional context, please let me know!
Answered by
GPT-4o mini
Let's carefully go through the calculations again to ensure we get the correct result for the population growth problem.
### Given:
- Initial population \( P_0 = 17,000 \)
- Growth rate \( r = 4\% = 0.04 \)
- Time \( t = 5 \) years
### Formula for Exponential Growth:
\[
P(t) = P_0 \times (1 + r)^t
\]
### Calculation Steps:
1. **Substitute values into the formula**:
\[
P(5) = 17000 \times (1 + 0.04)^5
\]
\[
P(5) = 17000 \times (1.04)^5
\]
2. **Calculate \( (1.04)^5 \)**:
\[
(1.04)^5 = 1.04 \times 1.04 \times 1.04 \times 1.04 \times 1.04
\]
Let's calculate that step-by-step:
- \( 1.04 \times 1.04 = 1.0816 \)
- \( 1.0816 \times 1.04 = 1.124864 \)
- \( 1.124864 \times 1.04 \approx 1.16985856 \)
- \( 1.16985856 \times 1.04 \approx 1.216652902 \)
Thus, we have:
\[
(1.04)^5 \approx 1.216652902
\]
3. **Now calculate \( P(5) \)**:
\[
P(5) \approx 17000 \times 1.216652902 \approx 20684.10934
\]
4. **Round this to the nearest whole number**:
\[
P(5) \approx 20684
\]
### Conclusion:
So, after checking the calculations carefully, it confirms again that the population after 5 years, rounded to the nearest whole number, is:
\[
\boxed{20684}
\]
If you're looking for something specific that seems incorrect, kindly let me know, and I'll address it!
### Given:
- Initial population \( P_0 = 17,000 \)
- Growth rate \( r = 4\% = 0.04 \)
- Time \( t = 5 \) years
### Formula for Exponential Growth:
\[
P(t) = P_0 \times (1 + r)^t
\]
### Calculation Steps:
1. **Substitute values into the formula**:
\[
P(5) = 17000 \times (1 + 0.04)^5
\]
\[
P(5) = 17000 \times (1.04)^5
\]
2. **Calculate \( (1.04)^5 \)**:
\[
(1.04)^5 = 1.04 \times 1.04 \times 1.04 \times 1.04 \times 1.04
\]
Let's calculate that step-by-step:
- \( 1.04 \times 1.04 = 1.0816 \)
- \( 1.0816 \times 1.04 = 1.124864 \)
- \( 1.124864 \times 1.04 \approx 1.16985856 \)
- \( 1.16985856 \times 1.04 \approx 1.216652902 \)
Thus, we have:
\[
(1.04)^5 \approx 1.216652902
\]
3. **Now calculate \( P(5) \)**:
\[
P(5) \approx 17000 \times 1.216652902 \approx 20684.10934
\]
4. **Round this to the nearest whole number**:
\[
P(5) \approx 20684
\]
### Conclusion:
So, after checking the calculations carefully, it confirms again that the population after 5 years, rounded to the nearest whole number, is:
\[
\boxed{20684}
\]
If you're looking for something specific that seems incorrect, kindly let me know, and I'll address it!
Answered by
GPT-4o mini
To solve the problem, let's define the variables based on the scenario given.
1. **Independent Variable (x)**: This typically represents the input or the quantity we can control. In this case, it represents the **number of questions answered correctly** on the test. So, we can state:
- The independent variable, \( x \), represents the **number of questions answered correctly**.
2. **Dependent Variable**: This variable depends on the independent variable. It reflects the result of the independent variable when plugged into a function. Here, the score on the test depends on how many questions are answered correctly.
- The dependent variable is the **score on the test**.
Thus, we can conclude:
- The dependent variable, \( y \), is the **score**, because the **score depends on the number of questions answered correctly**.
3. **Function relating these variables**: Since each correctly answered question is worth 3 points, we can write the function that relates the number of questions answered correctly (\( x \)) and the score (\( Q(x) \)) in the following manner:
\[
Q(x) = 3x
\]
4. **Calculating \( Q(17) \)**: Now we calculate the score if 17 questions are answered correctly:
\[
Q(17) = 3 \times 17 = 51
\]
Putting it all together, we have:
- The independent variable, \( x \), represents the **number of questions answered correctly**.
- The dependent variable is the **score on the test**, because the **score depends on the number of questions answered correctly**.
- A function relating these variables is \( Q(x) = 3x \).
- So \( Q(17) = 51 \), meaning when 17 questions are answered correctly, the score is **51**.
Here are your requested statements completed:
1. The independent variable, \( x \), represents the **number of questions answered correctly**.
2. The dependent variable is the **score on the test**, because the **score depends on the number of questions answered correctly**.
3. A function relating these variables is \( Q(x) = 3x \).
4. So \( Q(17) = 51 \), meaning when 17 questions are answered correctly, the score is **51**.
1. **Independent Variable (x)**: This typically represents the input or the quantity we can control. In this case, it represents the **number of questions answered correctly** on the test. So, we can state:
- The independent variable, \( x \), represents the **number of questions answered correctly**.
2. **Dependent Variable**: This variable depends on the independent variable. It reflects the result of the independent variable when plugged into a function. Here, the score on the test depends on how many questions are answered correctly.
- The dependent variable is the **score on the test**.
Thus, we can conclude:
- The dependent variable, \( y \), is the **score**, because the **score depends on the number of questions answered correctly**.
3. **Function relating these variables**: Since each correctly answered question is worth 3 points, we can write the function that relates the number of questions answered correctly (\( x \)) and the score (\( Q(x) \)) in the following manner:
\[
Q(x) = 3x
\]
4. **Calculating \( Q(17) \)**: Now we calculate the score if 17 questions are answered correctly:
\[
Q(17) = 3 \times 17 = 51
\]
Putting it all together, we have:
- The independent variable, \( x \), represents the **number of questions answered correctly**.
- The dependent variable is the **score on the test**, because the **score depends on the number of questions answered correctly**.
- A function relating these variables is \( Q(x) = 3x \).
- So \( Q(17) = 51 \), meaning when 17 questions are answered correctly, the score is **51**.
Here are your requested statements completed:
1. The independent variable, \( x \), represents the **number of questions answered correctly**.
2. The dependent variable is the **score on the test**, because the **score depends on the number of questions answered correctly**.
3. A function relating these variables is \( Q(x) = 3x \).
4. So \( Q(17) = 51 \), meaning when 17 questions are answered correctly, the score is **51**.
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