Answer :
To solve this question, we need to analyze the relationship between the distance [tex]\( d \)[/tex] and the time [tex]\( t \)[/tex] that Marlene rides her bike.
1. Statement Analysis:
- The independent variable, the input, is the variable [tex]\( d \)[/tex], representing distance.
- This statement is incorrect. In this scenario, the time [tex]\( t \)[/tex] Marlene rides her bike is the independent variable (input), and the distance [tex]\( d \)[/tex] traveled is the dependent variable (output).
- The distance traveled depends on the amount of time Marlene rides her bike.
- This statement is correct. The distance [tex]\( d \)[/tex] is a function of time [tex]\( t \)[/tex]. As Marlene rides her bike for more time, the distance she travels increases.
- The initial value of the scenario is 16 miles per hour.
- This statement is incorrect. The rate of 16 miles per hour is not an initial value; instead, it is the rate at which Marlene rides her bike. An initial value would refer to a starting distance at time [tex]\( t = 0 \)[/tex], which in this context is zero.
- The equation [tex]\( t = d + 16 \)[/tex] represents the scenario.
- This statement is incorrect. The correct mathematical relationship should be distance [tex]\( d \)[/tex] equals the rate (16 miles per hour) times the time [tex]\( t \)[/tex]. The equation provided does not correctly represent this relationship.
- The function [tex]\( f(t) = 16t \)[/tex] represents the scenario.
- This statement is correct. The distance [tex]\( d \)[/tex] can be represented by the function [tex]\( f(t) = 16t \)[/tex], indicating that the distance traveled by Marlene is the product of her rate (16 miles per hour) and the time [tex]\( t \)[/tex] in hours.
2. Conclusions:
Based on the analysis, the two statements that are true for the scenario are:
1. The distance traveled depends on the amount of time Marlene rides her bike.
2. The function [tex]\( f(t) = 16t \)[/tex] represents the scenario.
These two statements accurately describe the relationship between the time Marlene rides her bike and the distance she covers.
1. Statement Analysis:
- The independent variable, the input, is the variable [tex]\( d \)[/tex], representing distance.
- This statement is incorrect. In this scenario, the time [tex]\( t \)[/tex] Marlene rides her bike is the independent variable (input), and the distance [tex]\( d \)[/tex] traveled is the dependent variable (output).
- The distance traveled depends on the amount of time Marlene rides her bike.
- This statement is correct. The distance [tex]\( d \)[/tex] is a function of time [tex]\( t \)[/tex]. As Marlene rides her bike for more time, the distance she travels increases.
- The initial value of the scenario is 16 miles per hour.
- This statement is incorrect. The rate of 16 miles per hour is not an initial value; instead, it is the rate at which Marlene rides her bike. An initial value would refer to a starting distance at time [tex]\( t = 0 \)[/tex], which in this context is zero.
- The equation [tex]\( t = d + 16 \)[/tex] represents the scenario.
- This statement is incorrect. The correct mathematical relationship should be distance [tex]\( d \)[/tex] equals the rate (16 miles per hour) times the time [tex]\( t \)[/tex]. The equation provided does not correctly represent this relationship.
- The function [tex]\( f(t) = 16t \)[/tex] represents the scenario.
- This statement is correct. The distance [tex]\( d \)[/tex] can be represented by the function [tex]\( f(t) = 16t \)[/tex], indicating that the distance traveled by Marlene is the product of her rate (16 miles per hour) and the time [tex]\( t \)[/tex] in hours.
2. Conclusions:
Based on the analysis, the two statements that are true for the scenario are:
1. The distance traveled depends on the amount of time Marlene rides her bike.
2. The function [tex]\( f(t) = 16t \)[/tex] represents the scenario.
These two statements accurately describe the relationship between the time Marlene rides her bike and the distance she covers.
