Question
Henry earns $0.50 in interest from his savings account every year. Is this an example of a linear or exponential relationship? If so then which equation best fits.
Equation:
f(x)=1.5x 5
f(x)=2x+100 4 = 7
f(x)=0.5x 3
f(x)=100x 2
f(x)=100(0.5)^x
f(x)=100(0.98)^x
f(x)=100(1.5)^x
f(x)=100(2)^x
Equation:
f(x)=1.5x 5
f(x)=2x+100 4 = 7
f(x)=0.5x 3
f(x)=100x 2
f(x)=100(0.5)^x
f(x)=100(0.98)^x
f(x)=100(1.5)^x
f(x)=100(2)^x
Answers
GPT-4o mini
Henry's earnings of $0.50 in interest from his savings account every year represent a linear relationship because the interest earned increases by the same amount (a constant, $0.50) each year.
In mathematical terms, a linear relationship can typically be expressed in the form \( f(x) = mx + b \), where \( m \) is the slope (the amount of increase per unit) and \( b \) is the y-intercept.
Looking at the provided equations, we should identify the one that represents a linear relationship.
None of the provided equations explicitly fits the linear equation form \( f(x) = 0.5x + b \). However, we can see that since Henry earns a constant amount of interest ($0.50 per year), a simplified linear equation could be \( f(x) = 0.5x \) (if we take \( b = 0 \)).
Among the listed equations, the closest linear relationship in shape is:
- \( f(x) = 0.5x \)
If you meant to represent it as \( f(x) = 0.5x + 0 \), it would express that Henry earns $0.50 per year (assuming \( x \) represents the number of years).
In summary, the relationship is linear, and the best fit from your given options is \( f(x) = 0.5x \).
In mathematical terms, a linear relationship can typically be expressed in the form \( f(x) = mx + b \), where \( m \) is the slope (the amount of increase per unit) and \( b \) is the y-intercept.
Looking at the provided equations, we should identify the one that represents a linear relationship.
None of the provided equations explicitly fits the linear equation form \( f(x) = 0.5x + b \). However, we can see that since Henry earns a constant amount of interest ($0.50 per year), a simplified linear equation could be \( f(x) = 0.5x \) (if we take \( b = 0 \)).
Among the listed equations, the closest linear relationship in shape is:
- \( f(x) = 0.5x \)
If you meant to represent it as \( f(x) = 0.5x + 0 \), it would express that Henry earns $0.50 per year (assuming \( x \) represents the number of years).
In summary, the relationship is linear, and the best fit from your given options is \( f(x) = 0.5x \).