The number of US. citizens aged 65 years and older from 1900 through 2050 is estimated to be growing at the rate of $R(t)=0.063 t^{2}-0.48 t+3.87$ $(0 \leq t \leq 15)$ million people/decade, where t is measured in decades, with t=0 corresponding to 1900. Show that the average rate of growth of U.S. citizens aged 65 years and older between 2000 and 2050 will be about twice the average rate between 1950 and 2000.

Use the data to (a) find the coefficient of determination $r^2$ and interpret the result, and (b) find the standard error of estimates, and interpret the result. The table shows the combined city and highway fuel efficiency (in miles per gallon gasoline equivalent) and top speeds (in miles per hour) for nine hybrid and electric cars. The regression equation is $\hat{y}=-0.465 x+139.433$

$$\begin{matrix} \text{Fuel efficiency, x} & \text{114} & \text{95} & \text{120} & \text{105} & \text{107} & \text{116} & \text{118} & \text{68} & \text{84}\\ \text{Top speed, y} & \text{80} & \text{103} & \text{78} & \text{85} & \text{92} & \text{88} & \text{92} & \text{105} & \text{101}\\ \end{matrix}$$

For the following exercise, consider a rocket shot into the air that then returns to Earth. The height of the rocket in meters is given by $h(t)=600+78.4 t-4.9 t^{2}$, where t is measured in seconds. Use the preceding exercise to guess the instantaneous velocity of the rocket at t = 9 sec.