The table gives the U.S. population from 1790 to 1860.

$$\begin{array}{|c|c|} \hline Year & Popul.\\ \hline 1790 & 3,929,000\\ 1800 & 5,308,000\\ 1810 & 7,240,000\\ 1820 & 9,639,000\\ 1830 & 12,861,000\\ 1840 & 17,063,000\\ 1850 & 23,192,000\\ 1860 & 31,443,000\\ \hline \end{array}$$

Using a graphing calculator or computer to find an exponential model to the data:
(a) Estimate the rate of growth in 1800 to the nearest hundredth.
(b) Use part (a) to predict the population in 1870 to the nearest hundredth. (Compare with the actual population of 38,558,000. Can you explain the discrepancy?)

(a)
(b)