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: