Question

The height of a poplar tree in feet at age t years can be modeled by the function ℎ()=6+3(+1) . Use the model to predict the number of years when the height will exceed 17 feet.

Answer 1

To predict when the height of the poplar tree will exceed 17 feet, we can use the function h(t) = 6 + 3(t + 1). By substituting 17 for h(t) and solving for t, we find that the height will exceed 17 feet after approximately 4.67 years.

Step-by-step explanation:

To predict when the height of the poplar tree will exceed 17 feet, we need to find the value of t that satisfies the inequality h(t) > 17. The function that models the height of the poplar tree is h(t) = 6 + 3(t + 1).

We can substitute h(t) with 17 and solve for t:

17 = 6 + 3(t + 1)

17 = 6 + 3t + 3

14 = 3t

t = 4.67

Therefore, the height of the poplar tree will exceed 17 feet after approximately 4.67 years.