A local hospital estimates the weight of a new-born baby is given by the followi

ID: 1168229 • Letter: A

Question

A local hospital estimates the weight of a new-born baby is given by the following:

Weight = 1.17 + 0.76(Length)

where Weight is the measured in pounds and Length is measured in inches.

What is the predicted difference in weight for a baby that is 0.85 inches longer?
Answer: .65

A local utility estimates that natural gas consumption by an average household is given by the following:

Usage = 1.55 - 0.55(Price)

where Usage is the number of mcf consumed and Price measures the price of natural gas per mcf.

What is the predicted change in usage if the price decreases by 0.3 dollars? Answer .17

Can someone please explain this to me? I dont understand.

A local utility estimates that natural gas consumption by an average household is given by the following:

Usage = 1.55 - 0.55(Price)

where Usage is the number of mcf consumed and Price measures the price of natural gas per mcf.

What is the predicted change in usage if the price decreases by 0.3 dollars? Answer .17

Therefore the change in the prediction for the weight depends upon the change in the length of the new-born.

From the equation: Weight = 1.17 + 0.76 * Length, we can write the changes in weight as follows—

d (Weight) = 0.76 * d (Length)

Where, ‘d’ shows the change.

Now, for a baby who is 0.85 inches longer, that is, d (Length) = 0.85, we can say that the predicted difference in the Weight of the baby would be,

d (Weight) = 0.76 * 0.85 pounds

= 0.646 pounds

= 0.65 pounds

2. A local utility estimates the natural gas consumption by an average household by the following equation:

Usage = 1.55 – 0.55 * Price

This means the Usage of natural gas depends upon the Price of it. So, if the price of the natural gas changes, the Usage will change as well.

Therefore, we can write the predicted change in usage due to change in the price of natural gas by the following equation:

d (Usage) = - 0.55 * d (Price)

Now it was given that the decrease in price of gas is $0.3. So, we can write, d (Price) = - 0.3.

We have used the negative sign to indicate the decrease in price level.

Therefore, the change in the usage of natural gas would be,

d (Usage) = - 0.55 * (- 0.3)

= 0.165 mcf

= 0.17 mcf.

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