Question

PLEASE HELP ME WITH PROBLEM C

1) The Magnolia trees purchased for planting at the school are 3 feet tall. Research shows that these types of trees grow at an average rate of 3/4 feet per year.

a) Write an equation in Slope-Intercept form to represent the growth of the trees over time. Let x represent the number of years and let y represent the height (in ft.) of the tree.
Y=3/4x+3

b) What does the y-intercept represent in your equation
Y=3. 3 stands for feet tall


c) Determine the height of the tree in 3 years.​

Answer 1

a) To write an equation in slope-intercept form to represent the growth of the Magnolia trees over time, we can use the formula y = mx + b, where x represents the number of years, y represents the height of the tree in feet, m represents the slope (or rate of growth) of the tree, and b represents the y-intercept (or the height of the tree at x = 0).

In this case, the slope (m) of the tree is 3/4 feet per year and the y-intercept (b) is 3 feet, as the trees are initially 3 feet tall when they are purchased. Plugging these values into the formula gives us:

y = (3/4)x + 3

This equation represents the growth of the Magnolia trees over time.

b) The y-intercept of an equation in slope-intercept form represents the value of y when x is equal to 0. In this case, the y-intercept of the equation y = (3/4)x + 3 is 3 feet. This means that when x is equal to 0 (when no years have passed), the height of the tree is 3 feet.

c) To determine the height of the tree in 3 years, we can substitute 3 for x in the equation y = (3/4)x + 3 and solve for y. This gives us:

y = (3/4)(3) + 3

= 9/4 + 3

= 21/4

= 5.25 feet

Therefore, the height of the tree in 3 years is approximately 5.25 feet.