question: The population P of Canada from 1994 to 2002 is...

[bballj228]

The population P (in thousands) of Canada from 1994 to 2002 is shown in the table.

Year P
1994 29,036
1996 29,672
1998 30,248
2000 30,791
2002 31,414

Estimate the instantaneous rate of growth in 2000 by taking the average of two average rates of change. What are its units?

Estimate the instantaneous rate of growth in 2000 by measuring the slope of a tangent.

 

[tkhunny]

Estimate the instantaneous rate of growth in 2000 by taking the average of two average rates of change. What are its units?

Well, do it! What are the surrounding averages?

Estimate the instantaneous rate of growth in 2000 by measuring the slope of a tangent.

This cannot be done. A "tangent" requires a curve. Doe you mean "estimate" the slope of the tangent?

 

[Deleted member 4993]

The population P (in thousands) of Canada from 1994 to 2002 is shown in the table.

Year P
1994 29,036
1996 29,672
1998 30,248
2000 30,791
2002 31,414

Estimate the instantaneous rate of growth in 2000 by taking the average of two average rates of change. What are its units?

Estimate the instantaneous rate of growth in 2000 by measuring the slope of a tangent.

For the above, you can derive the equation of the curve in the following form:

y = Ax^4 + Bx^3 + Cx^2 + Dx + E

from the given data.

Then you can differentiate the curve at the given point to estimate the slope of the tangent line.

Have you been taught that method?