Question

When Marcia was born, she weighed 8 pounds. At 8 months, she

weighed 20 pounds. If she continues to grow at the same rate, how many
pounds will Marcia weigh when she becomes 1 year old?

Answer 1

Marcia will be 26 pounds when she is 1 year old

Explanation:

We are told to estimate Marcia's weight when she becomes 1 year old assuming the rate of change in weight over age (in months) continues to be that of the one observed between birth and when she was 8 months old.

We need then to calculate that rate of change which is what is going to be the "slope" (m) of a linear function that represents Marci's weight as a function of how many months old she is.

If we imagine then a coordinate system that represents Marcia's weight (in pounds) in the vertical axis, and age (in months) in the horizontal axis, the two pieces of information they give us are two (x,y) points on that plane:

When she was born (0 months old) her weight was 8 pounds. So this represents the point (0, 8) on that plane. The horizontal "x" coordinate representing age in months and the vertical "y" representing weight in pounds.

The information on her weight (20 pounds) when she is 8 months old, is given by the point (8, 20)

The slope of the segment of line connecting these points can be calculated with the formula:

`slope=(y_2-y_1)/(x_2-x_1) \\slope=(20-8)/(8-0) \\slope=(12)/(8) \\slope=(3)/(2)`

So now we build the line using this slope and one of the points we have created (0,8), by using the point-slope form of a line:

`y-y_0=m\,(x-x_0)\\y-8=(3)/(2) \.(x-0)\\y-8=(3)/(2)x\\y=(3)/(2)x+8`

and we can use it to predict Marcia's weight when she is 1 year old (notice here that we need to use "12" in the evaluation of her weight, since the x value (age) has to be entered in months:

`y=(3)/(2) (12)+8\\y=(36)/(2) +8\\y=18+8\\y=26`

Therefore, Marcia will be 26 pounds when she is 1 year old.