Question

In the third month of a study, a sugar maple tree is 82 inches tall. In the seventh month, the tree is 92 inches tall. Assuming the tree grows at a constant rate every month, what is the rule for the height of the tree during the nth month

Answer 1

The linear equation that gives the height on the x-th month is:

y = 2.5*x + 74.5

Which rule gives the height of the tree for the n-th month?

This will be modeled with a linear equation of the form:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that for a line with the points (x₁, y₁) and (x₂, y₂), the slope is given by:

$a = \frac{y_2 - y_1}{x_2 - x_1}$

Here we have the two points (3, 82) and (7, 92). Where the first value is the number of months and the second value is the height.

So the slope is:

$a = \frac{92 - 82}{7 - 3} = 10/4 = 2.5$

Then the linear equation is:

y = 2.5*x + b

To get the value of b, we use the fact that when x = 3, we have y = 82,

82 = 2.5*3 + b

82 = 7.5 + b

82 - 7.5 = b = 74.5

Then the linear equation is:

y = 2.5*x + 74.5

If you want to learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1