Final answer:
The correct equation representing the growth of the tree, which was 2 feet tall when planted and grows at a constant rate of 1 foot per year, is h(t) = 2t + 1, which matches option c.
Step-by-step explanation:
The question involves writing an equation for the growth of a tree over time, which is a mathematics problem, specifically related to linear functions and their applications. Since the tree grew from 2 feet to 3 feet in one year, the rate of growth is 1 foot per year. The tree's height after a certain number of years, t, can be given by h(t) which represents the height of the tree at time t. We are looking for an equation that starts with a height of 2 feet at year 0 (when the tree was planted) and increases by 1 foot each year.
To find the correct equation, we can examine the choices presented. Option a. h(t) = 2t + 3 does not fit the given parameters as it would mean the tree was 3 feet tall at year 0 and grows at a rate of 2 feet per year. Option b. h(t) = 2t - 1, also does not fit because it suggests that the tree was 1 foot tall when planted and grows at double the correct rate. Similarly, d. h(t) = 2t - 3 implies the tree was 3 feet tall when planted and would be negative at time 0, which does not make sense. Therefore, the correct equation must be option c. h(t) = 2t + 1, where t represents years since the tree was planted and the tree height increases by 1 foot each year and starts at 2 feet tall at year 0.