Linear Extrapolation or Interpolation?

Section 1.3
Question 98

See attachment.

I see two points in the form (t, y):

(1, 970) and (2, 1270)

I need the slope m.

m = (1270 - 970)/(3 - 1)

m = 300/2

m = 150

I need the point-slope formula.

y - y_1 = m(t - t_1)

I need one of the points and m.

y - 970 = 150(t - 1)

y - 970 = 150t - 150

y = 150t - 150 + 970

y = 150t + 820

Part (a) has been completed.

Part (b)

The slope is 150 but I don't know what it tells me about weight gain.

Do you know?

Part (c)

Let t = 2

y = 150(2) + 820

y = 300 + 820

y = 1,220

The average brain weight is 1,220 grams.

You say?

A. Is this a linear extrapolation or linear interpolation?

B. What's the difference between the two mentioned in A?

 

(b) The units of the slope here are grams per year, so it tells you the change in brain weight over the change in years.

A. answer is: linear interpolation
Linear Extrapolation
you use data to plot scatter graph, then find the best fitting line
see the below screenshot:

The formula for linear interpolation is slope-point formula

see the below screenshot:

 

Is my work correct? I say yes.

 

yes, your work is correct

 

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