Onine Lesson Data were colected comparing the weight W,inpounds, of a yeliodn tu

Question

Onine Lesson Data were colected comparing the weight W,inpounds, of a yeliodn tuna to its length L-n ceremetery, t These data·represented in the table below. 4.1 160 (a) What is the average rate of change, in weight per centimeter of length, in going from a length of places.) 100 centimeters to a length of 110 centimeters? (Round your answer to three decima bycm s the average rate of change, in weight per centimeter, i going from 140 to 360 centimeters? (Round your a answer to three decimal places) (c) Judging from the data in the tablie, does an extra centimeter of length make more difference in weight for small large (d) Use the average rate of change to estimate the weight of a yellowin tuna that is 149 centimeters long. (Round your answer to two decimal places) (e) What is the average rate of change, in length per pound of weight, in going from a weight of 179 pounds to a weight of 256 pounds? (Round your answer to two decimal places) on what would you expect to be the length of a yellowfin tuna weighing 225 pounds?(Round your answer to two deon al places, lb Need Help?

Explanation / Answer

a. When the length of tuna increases from 100 to 110 cm it's weight increases from 42.5 to 56.8 lb.

So increase in length = 110-100 =10.
Corresponding increase in weight = 56.8 -42.5 = 14.30 lb
Thus average rate of change, in weight per centimeter = 14.30/10 = 1.430 lb/cm.

b. When the length of tuna increases from 140 to 160 cm it's weight increases from 119 to 179 lb.

Thus the increase in length = 160-140 =20 cm
Corresponding increase in weight = 179 -119 = 60 lb
Thus average rate of change, in weight per centimeter = 60/20 = 3.00 lb/cm.

c. Extra centimeter in length makes more difference in weight of large tuna than a small tuna.

If we consider the parts a) and b) from above. The weight of smaller tunas (that is 100-110) on an average differ by 1.430 lb per cm whereas in larger tunas (140-160 cm) the average change in weight per centimeter is 3 lb.

So an extra centimeter in length shall make more difference in large tunas.

d.)

We saw in part b) that the average change in weight between 140 and 160 cm is 3lb per cm.

So we may estimate the weight of tuna of length 149 cm as follows;

Weight at 149 = weight at 140 + rate of change of weight (change in length)
                        = 119 + 3 (149-140) = 119+3*9 = 119+27 = 146.00 lb.

e)
When the length of tuna increases from 160 to 180 cm it's weight increases from 179 to 256 lb.
Thus the increase in length = 180-160 =20 cm
Corresponding increase in weight = 256-179 = 77 lb
Thus average rate of change, in weight per centimeter = 77/20 = 3.85 lb/cm.

f)

From above we have that the average change in weight per cm within length range 160-180 and weight range 160-180 is 3.85 lb/cm.

It is given that a tuna weighs 225 lb. We need to estimate it's length.

As we did above;
The weight of tuna = weight of tuna of length 160 cm + rate of change in weight*difference in length,
where difference in length is, actual length - 160.

Here we know weight of tuna, we need to find difference in length. Let difference length be d,

Then we have
225 = 179 + 3.85* d

So d = (225-179)/3.85 = 46/3.85 = 11.95 cm.

Thus the length of a tuna of weight 225 lb is 160+11.95 = 171.95 cm.

So answer is 171.95 cm.

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