The yearly production of a 5 foot tree is 25 oranges. A 16 foot tree produces 58 oranges. Firstly, I had to list the ordered pairs, which are (5,25) and (16,58)then used slope-point equation to find the number of fruits from 18 and 20 foot trees. The last part of the question is to predict the height of an orange tree that produces 88 number of fruits. What can I do here?

Question

The yearly production of a 5 foot tree is 25 oranges. A 16 foot tree produces 58 oranges. Firstly, I had to list the ordered pairs, which are (5,25) and (16,58)then used slope-point equation to find the number of fruits from 18 and 20 foot trees. The last part of the question is to predict the height of an orange tree that produces 88 number of fruits. What can I do here?

Answer 1

To find the number of fruits from 18 and 20 foot trees using the slope-point equation, you need to determine the equation of the line that represents the relationship between the height of the tree and the number of fruits produced.

In this case, you have two ordered pairs: (5, 25) and (16, 58). To find the slope, you can use the formula:

slope = (y2 - y1) / (x2 - x1)

Let's use the first ordered pair as (x1, y1) and the second ordered pair as (x2, y2):

slope = (58 - 25) / (16 - 5) = 33 / 11 = 3

Now that we have the slope, we can use the point-slope equation to find the number of fruits from 18 and 20 foot trees. The point-slope equation is:

y - y1 = m(x - x1)

Using the first ordered pair as (x1, y1) = (5, 25):

y - 25 = 3(x - 5)

Let's calculate for the number of fruits produced by an 18-foot tree:

y - 25 = 3(18 - 5)
y - 25 = 3(13)
y - 25 = 39
y = 39 + 25
y = 64

Therefore, the number of fruits produced by an 18-foot tree is 64.

Similarly, let's calculate for the number of fruits produced by a 20-foot tree:

y - 25 = 3(20 - 5)
y - 25 = 3(15)
y - 25 = 45
y = 45 + 25
y = 70

Therefore, the number of fruits produced by a 20-foot tree is 70.

Now, let's predict the height of an orange tree that produces 88 number of fruits.

Using the same slope and the point-slope equation, we can substitute the number of fruits (y) as 88:

88 - 25 = 3(x - 5)
63 = 3(x - 5)

Simplifying the equation:

63 = 3x - 15
3x = 63 + 15
3x = 78
x = 78 / 3
x = 26

Therefore, the predicted height of the orange tree that produces 88 number of fruits is 26 feet.

In summary:

- Number of fruits produced by an 18-foot tree: 64
- Number of fruits produced by a 20-foot tree: 70
- Predicted height of an orange tree that produces 88 number of fruits: 26 feet.