Tutorial Exercise A pet lamb grows rapidly, with its mass proportional to the cube of its length. When the lamb's length changes by 16.1%, its mass increases by 15.3 kg. Find the lamb's mass at the end of this process. Step 1 The little sheep's final mass must be a lot more than 15 kg, so an order of magnitude estimate is 100 kg. 1r this turns out to be true, the sheep is not so little anymore. Step 2 When the length changes by 16.1%, the mass changes by a much larger percentage. We will write each of the sentences in the problem as a mathematical equation. Step 3 Mass is proportional to length cubed: mk where is a constant. This model of growth is reasonable because the lamb gets thicker as it gets longer, growing in three dimensional space. At the initial and final points, m,- and m,A,, so Length changes by 16.1%. We know that 16.1% of t means 0.161 times f. So we have , yielding , From this, we have And finally, mass increases by 15.3 kg:
Tutorial Exercise A pet lamb grows rapidly, with its mass proportional to the cube of its length. When the lamb's length changes by 16.1%, its mass increases by 15.3 kg. Find the lamb's mass at the end of this process. Step 1 The little sheep's final mass must be a lot more than 15 kg, so an order of magnitude estimate is 100 kg. 1r this turns out to be true, the sheep is not so little anymore. Step 2 When the length changes by 16.1%, the mass changes by a much larger percentage. We will write each of the sentences in the problem as a mathematical equation. Step 3 Mass is proportional to length cubed: mk where is a constant. This model of growth is reasonable because the lamb gets thicker as it gets longer, growing in three dimensional space. At the initial and final points, m,- and m,A,, so Length changes by 16.1%. We know that 16.1% of t means 0.161 times f. So we have , yielding , From this, we have And finally, mass increases by 15.3 kg:
Related questions
Question
Transcribed Image Text:1.
DETAILS
ASK YOUR TEACHER
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come
back to the skipped part.
Tutorial Exercise
A pet lamb grows rapidly, with its mass proportional to the cube of its length. When the lamb's length changes by 16.1%, its mass increases by 15.3 kg. Find the lamb's mass at
the end of this process.
Step 1
The little sheep's final mass must be a lot more than 15 kg, so an order of magnitude estimate is 100 kg. If this turns out to be true, the sheep is not so little anymore.
Step 2
When the length changes by 16.1%, the mass changes by a much larger percentage. We will write each of the sentences in the problem as a mathematical equation.
Step 3
MY NOTES
Mass is proportional to length cubed: m kwhere k is a constant. This model of growth is reasonable because the lamb gets thicker as it gets longer, growing in three
dimensional space.
At the initial and final points, m,- and m,,, so
Length changes by 16.1%. We know that 16.1% of f means 0.161 times f. So we have
, yielding ,
From this, we have
And finally, mass increases by 15.3 kg:
m₂ +15.3 kg = my
Submit Stupyou cannot come back)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 4 images
