Question
Question 1 A)Graph the exponential function y=0.5(6)xy=0.5(6)x. Identify the y-intercept.(1 point) Responses −4−4 negative 4 0 0 0.5 0.5 1 1 Question 2 A)Graph the function y=5(14)xy=5(14)x. Complete the ordered pairs for the x-values of −2−2, −1−1, 0, and 1 by finding the y-values.(1 point) Responses (−2,−2.5)(−2,−2.5), (1,1.25)(1,1.25), (0,0)(0,0) and (1,1.2)(1,1.2) left parenthesis negative 2 comma negative 2.5 right parenthesis , left parenthesis 1 comma 1.25 right parenthesis , left parenthesis 0 comma 0 right parenthesis and left parenthesis 1 comma 1.2 right parenthesis (−2,0.45)(−2,0.45), (−1,0.67)(−1,0.67), (0,1)(0,1), and (1,1.50)(1,1.50) left parenthesis negative 2 comma 0.45 right parenthesis , left parenthesis negative 1 comma 0.67 right parenthesis , left parenthesis 0 comma 1 right parenthesis , and left parenthesis 1 comma 1.50 right parenthesis (−2,−2.99)(−2,−2.99), (−1,−1.49)(−1,−1.49), (0,0)(0,0), and (1,1.49)(1,1.49) left parenthesis negative 2 comma negative 2.99 right parenthesis , left parenthesis negative 1 comma negative 1.49 right parenthesis , left parenthesis 0 comma 0 right parenthesis , and left parenthesis 1 comma 1.49 right parenthesis (−2,80)(−2,80), (−1,20)(−1,20), (0,5)(0,5), and (1,1.25)
Answers
GPT-4o mini
Let's work through each question step by step.
### Question 1
The given exponential function is \( y = 0.5(6^x) \).
1. **Y-Intercept**:
To find the y-intercept, set \( x = 0 \):
\[
y = 0.5(6^0) = 0.5(1) = 0.5.
\]
Thus, the y-intercept is \( (0, 0.5) \).
**Response**: The y-intercept is \( 0.5 \).
### Question 2
The given exponential function is \( y = 5(14^x) \). We need to calculate the y-values for the x-values of \( -2, -1, 0, \) and \( 1 \).
1. For \( x = -2 \):
\[
y = 5(14^{-2}) = 5\left(\frac{1}{14^2}\right) = 5\left(\frac{1}{196}\right) = \frac{5}{196} \approx 0.0255.
\]
2. For \( x = -1 \):
\[
y = 5(14^{-1}) = 5\left(\frac{1}{14}\right) = \frac{5}{14} \approx 0.3571.
\]
3. For \( x = 0 \):
\[
y = 5(14^0) = 5(1) = 5.
\]
4. For \( x = 1 \):
\[
y = 5(14^1) = 5(14) = 70.
\]
Now we can compile the ordered pairs:
- \((-2, 0.0255)\)
- \((-1, 0.3571)\)
- \((0, 5)\)
- \((1, 70)\)
From the responses you provided, the closest approximation for ordered pairs would likely be:
\((−2, 0.45), (−1, 0.67), (0, 5), (1, 1.50)\) seems wrong based on the calculations above.
None of the sets provided seem to match the values. The correct values are:
- \((-2, 0.0255)\),
- \((-1, 0.3571)\),
- \((0, 5)\),
- \((1, 70)\).
Unfortunately, none of the options correctly reflect the calculated y-values for \( y = 5(14^x) \).
To answer, we conclude:
- **The y-values for x = -2, -1, 0, and 1 are approximately \( (−2, 0.0255) \), \( (−1, 0.3571) \), \( (0, 5) \), \( (1, 70) \)**.
### Question 1
The given exponential function is \( y = 0.5(6^x) \).
1. **Y-Intercept**:
To find the y-intercept, set \( x = 0 \):
\[
y = 0.5(6^0) = 0.5(1) = 0.5.
\]
Thus, the y-intercept is \( (0, 0.5) \).
**Response**: The y-intercept is \( 0.5 \).
### Question 2
The given exponential function is \( y = 5(14^x) \). We need to calculate the y-values for the x-values of \( -2, -1, 0, \) and \( 1 \).
1. For \( x = -2 \):
\[
y = 5(14^{-2}) = 5\left(\frac{1}{14^2}\right) = 5\left(\frac{1}{196}\right) = \frac{5}{196} \approx 0.0255.
\]
2. For \( x = -1 \):
\[
y = 5(14^{-1}) = 5\left(\frac{1}{14}\right) = \frac{5}{14} \approx 0.3571.
\]
3. For \( x = 0 \):
\[
y = 5(14^0) = 5(1) = 5.
\]
4. For \( x = 1 \):
\[
y = 5(14^1) = 5(14) = 70.
\]
Now we can compile the ordered pairs:
- \((-2, 0.0255)\)
- \((-1, 0.3571)\)
- \((0, 5)\)
- \((1, 70)\)
From the responses you provided, the closest approximation for ordered pairs would likely be:
\((−2, 0.45), (−1, 0.67), (0, 5), (1, 1.50)\) seems wrong based on the calculations above.
None of the sets provided seem to match the values. The correct values are:
- \((-2, 0.0255)\),
- \((-1, 0.3571)\),
- \((0, 5)\),
- \((1, 70)\).
Unfortunately, none of the options correctly reflect the calculated y-values for \( y = 5(14^x) \).
To answer, we conclude:
- **The y-values for x = -2, -1, 0, and 1 are approximately \( (−2, 0.0255) \), \( (−1, 0.3571) \), \( (0, 5) \), \( (1, 70) \)**.