Question

fertilizer amounts, heights of plants, and fruit yield of plants
fertilizer (oz) | height of tree
(in )
180 | 95
190 | 101
150 | 83
120 | 64
140 | 76

fertilizer (oz) | amount of fruit
produced (lb)
180 | 220
190 | 231
150 | 177
120 | 132
140 | 158

$y = 0.5x + 4$

$y = 1.4x - 42$

if a tree is given the fertilizer and grows to 80 inches, how much fruit is the tree expected to produce?
20
87
166
171

Explanation:

Step1: Find fertilizer amount (x) using height formula.

Given height formula \( y = 0.5x + 4 \), and \( y = 80 \) (height of tree).
Substitute \( y = 80 \):
\( 80 = 0.5x + 4 \)
Subtract 4: \( 76 = 0.5x \)
Multiply by 2: \( x = 152 \)? Wait, no—wait, solve \( 80 = 0.5x + 4 \):
\( 0.5x = 80 - 4 = 76 \)
\( x = 76 \div 0.5 = 152 \)? Wait, no, 76 * 2 = 152? Wait, 0.5x = 76 → x = 152? Wait, maybe I made a mistake. Wait, the first table is fertilizer (oz) and height (in). The equation is \( y = 0.5x + 4 \), where y is height (in), x is fertilizer (oz). So if height y = 80, find x:

\( 80 = 0.5x + 4 \)
\( 0.5x = 80 - 4 = 76 \)
\( x = 76 \times 2 = 152 \)? Wait, but the first table has fertilizer amounts 180, 190, 150, 120, 140. 152 is close to 150, but let's proceed.

Step2: Use fruit formula with x (fertilizer) to find fruit yield.

Fruit formula: \( y = 1.4x - 42 \), where x is fertilizer (oz), y is fruit (lb).
Substitute x = 152:
\( y = 1.4 \times 152 - 42 \)
Calculate 1.4 152: 152 1.4 = 212.8
Then 212.8 - 42 = 170.8 ≈ 171. Wait, but maybe I messed up the first step. Wait, maybe the first equation is height (y) in terms of fertilizer (x). So if height is 80, find x (fertilizer) using \( y = 0.5x + 4 \). So:

\( 80 = 0.5x + 4 \)
\( 0.5x = 76 \)
\( x = 152 \). Then plug into fruit formula: \( 1.4*152 - 42 = 212.8 - 42 = 170.8 ≈ 171 \). So the answer is 171.

Wait, but let's check again. Maybe I made a mistake in the first step. Wait, the first table: fertilizer (x) and height (y). The equation is \( y = 0.5x + 4 \). So for x=150, y=0.5*150 +4=75+4=79? But the table says 83. Hmm, maybe the equation is a model, not exact. So proceed with the model.

So step1: find x when y=80 (height) using \( y = 0.5x + 4 \).
Step2: plug x into \( y = 1.4x - 42 \) to find fruit yield.

So step1:
\( 80 = 0.5x + 4 \)
\( 0.5x = 76 \)
\( x = 152 \)

Step2:
\( y = 1.4*152 - 42 = 212.8 - 42 = 170.8 ≈ 171 \). So the answer is 171.

Answer:

171