According to the census, the number of inhabitants of the U.S. over the period 1790 to 1850 was as follows.

Year Population (millions)

1790 3.929

1800 5.308

1810 7.240

1820 9.638

1830 12.866

1840 17.069

1850 23.192

Over this period, the population grew roughly exponentially. Taking t = 0 to correspond to the start of the year 1790, we can approximate the population size by the exponential curve

N(t) =N₀ e^kt

for some N₀ and k. Find the best fitting values of N₀ and k by taking natural logs of the population sizes and using linear regression. (Give your answers correct to at least four decimal places, but be careful to use the unrounded values when you calculate the answers to the last two parts of this problem!) N₀ = 3.9461 million people k = .02924 per year 1) According to the exponential curve, in what year would the population be predicted to reach one hundred million people? (Give a calendar year. For example: 1851) 2) What population size does the exponential curve predict for the start of the year 2015? (Give your answer correct to at least one decimal place.) million people