1. ## question

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.

2. Originally Posted by 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.
Just use the defintion of average rate of change

$m=\text{slope}=\frac{\Delta{y}}{\Delta{x}}$

As for the second one, its basicallyt the same thing.

3. Originally Posted by 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.
So lets find the rate of change from 1998 to 2000

$m_1=\frac{30791-30248}{2000-1998}=\frac{543}{2}$

and now from 2000 to 2002
$m_2=\frac{31414-30791}{2002-2000}=\frac{623}{2}$

Now we can take the average of these to get

$\frac{m_1+m_2}{2}=\frac{\frac{543}{2}+\frac{623}{2 }}{2}=\frac{1166}{4}=\frac{583}{2}=291.5$

The units would be $\frac{\mbox{change in population}}{\mbox{years}}$

4. Originally Posted by bballj228
Estimate the instantaneous rate of growth in 2000 by measuring the slope of a tangent.
For the second part you are going to have to graph the data and connect the points with a smooth curve. Then sketch in the tangent line to the curve at 2000. Then measure the slope of that line.

-Dan

5. thanks guys got it