We study the heart girth of beef cattle and find the following:hearth girth of 40 inch weighed 207 lbs heart g

Question

We study the heart girth of beef cattle and find the following:hearth girth of 40 inch weighed 207 lbs heart girth of 60 inches had weight of 649 lbs.

A. Find the formula relating heart girth (x) to weight (y).

B. What would the weight be for an animal with heart girth of 75 inches?

C. What is the heart girth for an animal weighing 1169 pounds?

Try to Show Your Work.

Answer 1

A. we know one additional thing: a cow with a heart girth of 0 would weigh 0. So the formula has to look something like
y = Ax^T
207 = A*40^t
649 = A*207^t
or
649/207 = (207/40)^t, or 3.13 = 5.1^t.
if we take the log of both sides, we get
ln(3.13) = tln(5.1), or t = ln(3.13)/lon(5.1)= .695
Substituting back, we get A = 207/(40^.695) = 15.9
Checking our work, we test each equation, and using excel, this works.

B. 320 (use the same formula)

C. to do this, we need to invert the formula y=Ax^t
take natural log of both sides again, lny = lna+tlnx
lnx = 1/t *(ln(y/A))
then take the exponent of both sides to get
x = exp(ln(y/A))^(1/t) = (y/A)^(1/t).
Plugging in 1169, we get 482 inches