Question
How can you find an approximate answer for the equation 10e0.1x=53
?(1 point)
Responses
Find the vertex of f(x)=10e0.1x
.
Find the vertex of f left parenthesis x right parenthesis equals 10 e superscript 0.1 x baseline .
Find the horizontal asymptote of f(x)=10e0.1x
and add it to 53.
Find the horizontal asymptote of f left parenthesis x right parenthesis equals 10 e superscript 0.1 x baseline and add it to 53.
Find the intersection of f(x)=10e0.1x
and g(x)=53
.
Find the intersection of f left parenthesis x right parenthesis equals 10 e superscript 0.1 x baseline and g left parenthesis x right parenthesis equals 53 .
Find the x-intercept of f(x)=10e0.1x
.
?(1 point)
Responses
Find the vertex of f(x)=10e0.1x
.
Find the vertex of f left parenthesis x right parenthesis equals 10 e superscript 0.1 x baseline .
Find the horizontal asymptote of f(x)=10e0.1x
and add it to 53.
Find the horizontal asymptote of f left parenthesis x right parenthesis equals 10 e superscript 0.1 x baseline and add it to 53.
Find the intersection of f(x)=10e0.1x
and g(x)=53
.
Find the intersection of f left parenthesis x right parenthesis equals 10 e superscript 0.1 x baseline and g left parenthesis x right parenthesis equals 53 .
Find the x-intercept of f(x)=10e0.1x
.
Answers
GPT-4o mini
To find an approximate solution for the equation \( 10e^{0.1x} = 53 \), the most suitable method from the options provided is:
**Find the intersection of \( f(x) = 10e^{0.1x} \) and \( g(x) = 53 \).**
This approach involves finding the value of \( x \) where the exponential function \( 10e^{0.1x} \) intersects the horizontal line \( y = 53 \). This can typically be evaluated graphically or by solving the equation algebraically:
1. Set the equations equal to each other: \( 10e^{0.1x} = 53 \).
2. Rearrange to isolate \( e^{0.1x} \): \( e^{0.1x} = \frac{53}{10} \).
3. Take the natural logarithm of both sides: \( 0.1x = \ln\left(\frac{53}{10}\right) \).
4. Solve for \( x \): \( x = \frac{\ln\left(\frac{53}{10}\right)}{0.1} \).
This will give you the approximate solution you are looking for.
**Find the intersection of \( f(x) = 10e^{0.1x} \) and \( g(x) = 53 \).**
This approach involves finding the value of \( x \) where the exponential function \( 10e^{0.1x} \) intersects the horizontal line \( y = 53 \). This can typically be evaluated graphically or by solving the equation algebraically:
1. Set the equations equal to each other: \( 10e^{0.1x} = 53 \).
2. Rearrange to isolate \( e^{0.1x} \): \( e^{0.1x} = \frac{53}{10} \).
3. Take the natural logarithm of both sides: \( 0.1x = \ln\left(\frac{53}{10}\right) \).
4. Solve for \( x \): \( x = \frac{\ln\left(\frac{53}{10}\right)}{0.1} \).
This will give you the approximate solution you are looking for.