Question

After it is planted, a tree grows at a rate of 0.8 meters per year. after 3 years the tree is 3.1 meters tall. write the equation in point-slope form that models the situation. then, predict the height of the tree after 5 years

Answer 1

The linear function, in point-slope form, that models the situation is:

$y - 3.1 = 0.8(x - 3)$

Using the function, in 5 years, the height is of 4.7 meters.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

In point-slope form, considering a point $(x_0, y_0)$, the equation is given by:

$y - y_0 = m(x - x_0)$

In this problem, we have that the slope and the point are given, respectively, as:

$m = 0.8, (x_0, y_0) = (3, 3.1)$

Hence the equation is:

$y - 3.1 = 0.8(x - 3)$

In 5 years, we have that x = 5, hence:

y = 3.1 + 0.8(5 - 3) = 4.7 meters.

More can be learned about linear functions at brainly.com/question/24808124

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