The Egg Problem. A certain zoo kept records of the
relationship between the weight of a mother ostrich and
the weight of her egg. Data for three birds is shown in
the next table.
a. Estimate the weight of an egg from a mother ostrich
weighing 175 lbs.
b. How much would you expect the egg to weigh from
a mother ostrich weighing 190 lbs?
We do not have the table to help you.
Ostrich 1 Ostrich 2 Ostrich 3
Weight of Mother 120 lbs. 160 lbs. 180 lbs.
Weight of Egg 2.4 lbs 3.2 lbs 3.6 lbs
Sorry about that.
From your data, form three ordered pairs
(120,2.4), (160,3.2) and (180,3.6)
there is a linear relation between the 3 points, they lie in a straight line.
So you can find the equation of egg weight (e) vs ostrich mother weight (w)
the slope between any two of the three points is .02
so e = .02w + b , (using the standard y=mx+b )
using (120,2.4)
2.4 = .02(120) + b
b = 0
so e = .02w ---- a direct variation.
so for a) sub in 175 for w to get
e = .02(175) = 3.5
You do b), ok?
Yup, I think I got it
e = .02(190) = 3.8 right?
To estimate the weight of an egg from a mother ostrich weighing 175 lbs, we can use the data provided in the table. The weight of the mother ostrich seems to have a linear relationship with the weight of her egg. We can assume that this relationship can be represented by a linear equation of the form:
Weight of Egg = m * Weight of Mother Ostrich + b
To find the values of m and b, we can use the data provided in the table.
Let's calculate the values of m and b using the two data points given in the table:
Data point 1: (120, 80)
Data point 2: (135, 90)
m = (Weight of Egg2 - Weight of Egg1) / (Weight of Mother Ostrich2 - Weight of Mother Ostrich1)
= (90 - 80) / (135 - 120)
= 10 / 15
= 2/3
Now, substitute the value of m into the equation and solve for b:
80 = (2/3) * 120 + b
80 = 80 + b
b = 80 - 80
b = 0
Therefore, the equation representing the relationship between the weight of the mother ostrich and the weight of her egg is:
Weight of Egg = (2/3) * Weight of Mother Ostrich
Now, we can use this equation to estimate the weight of an egg from a mother ostrich weighing 175 lbs.
Weight of Egg = (2/3) * 175
= 350/3
≈ 116.67 lbs
So, the estimated weight of the egg from a mother ostrich weighing 175 lbs is approximately 116.67 lbs.
To estimate the weight of an egg from a mother ostrich weighing 190 lbs, we can again use the equation:
Weight of Egg = (2/3) * Weight of Mother Ostrich
Weight of Egg = (2/3) * 190
= 380/3
≈ 126.67 lbs
So, we would expect the egg to weigh approximately 126.67 lbs from a mother ostrich weighing 190 lbs.