Question

Reuben is driving to New York City. Let (d) represent his distance from New York City (in miles), and (t) represent the time he has been driving (in hours). Suppose that (d) and (t) are related by the equation (d = 60t + 180).

a)(d) is the dependent variable, and (t) is the independent variable.
b)(d) is the independent variable, and (t) is the dependent variable.
c) The equation represents a linear relationship between distance and time.
d)The equation suggests an exponential growth model for Reuben's journey.

Answer 1

The question requires determining if distance (d) depends on the time (t) and if their relationship is either linear or exponential. The answer clarifies that distance is dependent on time, and the equation provided represents a linear relationship, not an exponential growth model.

Step-by-step explanation:

Based on the equation given, d = 60t + 180, we can analyze the relationship between the distance Reuben is from New York City and the time he has been driving. In this linear equation, d represents the distance from New York City, which is the dependent variable because it depends on the value of t, the time. Thus, (d) is the dependent variable, and (t) is the independent variable.

The equation represents a linear relationship between distance and time, indicated by the direct proportionality between t and d and by the presence of a constant (180), which is the y-intercept of the linear equation. This signifies that Reuben starts 180 miles away from New York City at time zero. The slope of the line, which is 60, represents Reuben's constant speed. There is no evidence to suggest an exponential model; hence, the equation does not suggest exponential growth for Reuben's journey.