On a snow day, Leah created two snowmen in her backyard. Snowman A was built to a height of 33 inches and Snowman B was built to a height of 57 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 3 inches per hour and Snowman B's height decreased by 9 inches per hour. Let A represent the height of Snowman A t hours after sunrise and let B represent the height of Snowman B t hours after sunrise. Graph each function and determine which Snowman is taller after 6 hours.
To graph the functions, we need to first write them in terms of t.
For Snowman A: A(t) = 33 - 3t
For Snowman B: B(t) = 57 - 9t
Now we can graph these functions and determine which snowman is taller after 6 hours.
Graphing A(t) = 33 - 3t, we get the following graph:
y-axis: Height of Snowman A
x-axis: Hours after sunrise (t)
The graph of A(t) is a straight line starting at the point (0, 33) and decreasing by 3 units per hour.
Next, graphing B(t) = 57 - 9t, we get the following graph:
y-axis: Height of Snowman B
x-axis: Hours after sunrise (t)
The graph of B(t) is also a straight line starting at the point (0, 57) and decreasing by 9 units per hour.
Now, we can determine the height of each snowman after 6 hours by plugging t=6 into the functions:
A(6) = 33 - 3(6) = 33 - 18 = 15 inches
B(6) = 57 - 9(6) = 57 - 54 = 3 inches
After 6 hours, Snowman A is taller as it has a height of 15 inches compared to Snowman B's height of 3 inches.