Question

a botanist is monitoring the growth of a young tree and notices it is growing linearly. In fact, she realizes it is growing 3 inches every week. Unfournately , she forgot to begin recording until well into the growing process. what she does know is that it is currently week 17 and the tree is currently 4 feet and 8 inches tall. use the info. to model the situation with an equation in point slope form sliplify the equation to slope intercept form how tall was the seedling of the tree when the botanist received it? how tall with the tree be on week 30?

Answer 1

1) The equation in point and slope form is y - 56 = 3·(x - 17)

2) The above equation in slope and intercept form is y = 3·x + 5

3) The height of the sidling when the botanist received it = 5 inches

4) The height of the tree on week 30 = 7 feet 11 inches

Explanation:

The given parameters for the equation are;

The rate of growth of the young tree = 3 inches/week

The current height of the tree = 4 feet 8 inches = 56 inches

The current time since start of growth (time duration of growth) = 17 weeks

With the given information, we have;

The height of the tree, y = The dependent or y-variable

The time for the growth, x = The independent or x-variable

The slope = the rate of growth = 3 inches/week

At week, x = 17, y = 56 inches

1) The information presented in point and slope form is given as follows;

y - 56 = 3·(x - 17)

2) Simplifying the above equation to slope and intercept form, y = mx + c

Where;

m = The slope

c = The y-intercept

We have;

y = 3·x - 51 + 56 = 3·x + 5

y = 3·x + 5

Therefore the y-intercept = 5

3) The y-intercept = 5 which gives the value of the height of the tree at time x = 0 as follows;

At x = 0 when the tree was first received, the height of the tree, y = 3·x + 5 = 5 inches

4) On week 30, the height, y of the tree will be, y = 3 × 30 + 5 = 95 inches = 7 feet 11 inches.