Determine whether each verbal description represents a linear function or not. Correct me if I'm wrong on any of these!!
1. Jova walks quickly for 25 minutes then she rests for 5 minutes before continuing on for another 10 minutes. (NOT A LINEAR FUNCTION)
2 A rock that is projected upward from ground level with an initial velocity of 90 feet per second. (LINEAR FUNCTION)
3.The total charges, T, of an auto mechanic and the number of hours, H, that he worked. (LINEAR FUNCTION)
4.The height of a dog jumping off a dock into a pond. (NOT A LINEAR FUNCTION)
5. The amount of water being drained from a reservoir at a rate of 200 gallons per minute (LINEAR FUNCTION)
#2 is like #4. Not linear. Assuming the function is its height.
1. To determine if the verbal description represents a linear function, we need to check if there is a constant rate of change. In this case, Jova walks quickly for 25 minutes, rests for 5 minutes, and then continues for another 10 minutes. The time intervals are not constant, so it does not represent a linear function. Your answer is correct.
2. The rock projected upward with an initial velocity of 90 feet per second represents a linear function. The height of the rock can be calculated using the equation h(t) = 90t - 16t², where t is the time in seconds. The equation has a constant rate of change of -16, making it a linear function. Your answer is correct.
3. The total charges of an auto mechanic and the number of hours worked represents a linear function. As the number of hours increases, the total charges will also increase at a constant rate. We can represent this relationship using the equation T = rH, where T is the total charges, H is the number of hours, and r is the hourly rate. Since the equation has a constant rate of change (r), it represents a linear function. Your answer is correct.
4. The height of a dog jumping off a dock into a pond does not represent a linear function. The height will change over time, and it may vary non-linearly based on factors such as the dog's motion, angle of jumping, and other physical phenomena. Your answer is correct.
5. The amount of water being drained from a reservoir at a rate of 200 gallons per minute represents a linear function. As time increases, the amount of water drained also increases at a constant rate of 200 gallons per minute. The equation representing this relationship would be W = 200t, where W is the amount of water drained and t is the time in minutes. Your answer is correct.