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# The table gives the US population from 1790 to 1860.(a) Use a graphing calculator or computer to fit an exponential function to the data. Graph the data points and the exponential model. How good is the fit?(b) Estimate the rates of population growth in 1800 and 1850 by averaging slopes of secant lines.(c) Use (he exponential model in part (a) to estimate the rates of growth in 1800 and 1850. Compare these estimates with the ones in part (b).(d) Use the exponential model to predict the population in 1870. Compare with the actual population of 38,358,000. Can you explain the discrepancy?

## a. $R^{2}=0.999$b. $$\begin{array}{l}{\text { For } 1800, m_{s e c}=165,550} \\ {\text { For } 1850, m_{s e c}=719,000}\end{array}$$c. $$\begin{array}{l}{\text { For } x=1800 : f^{\prime}(x)=169,757} \\ {\text { For } x=1850 : f^{\prime}(x)=742,016}\end{array}$$d. $45,375,883$

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