Question

A family planted a cherry tree in their backyard in 2013. Since then, the cherry tree has grown at a constant rate. In 2017, the tree was 14 feet tall. In 2019, the tree was 17.5 feet tall. Complete the equation that describes the relationship between the height of the tree in feet, H, and the elapsed time in years since 2013, t. Write your answer using whole numbers or decimals rounded to the nearest hundredth.

Answer 1

The equation that describes the relationship between the height of the tree and the elapsed time can be written as H = 14 + 1.75(t - 2017).

Step-by-step explanation:

To find the equation that describes the relationship between the height of the tree, H, and the elapsed time in years, t, since 2013, we can use the given information about the tree's growth. We know that in 2017, the tree was 14 feet tall, and in 2019, the tree was 17.5 feet tall.

1. We can determine the rate of growth by subtracting the initial height from the final height and dividing by the elapsed time: (17.5 - 14) / (2019 - 2017) = 3.5 / 2 = 1.75 feet per year.
2. Next, we can use the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. We can choose the point (2017, 14) and the slope 1.75 to write the equation: H - 14 = 1.75(t - 2017).
3. Simplifying the equation, we get H = 14 + 1.75(t - 2017).