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 ekt 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!)

Step-by-step explanation:

This question is incomplete. I have attached a complimentary image of the census which captures the number of inhabitants of the U.S over the period 1790 to 1850. The data captured in this attachment completes the question.

From the question, it is given that

where and are constant

Note that

 and so it goes on ...

Therefore, for the year 1790,

And for the year 1800,

Taking the natural log on both sides, we get

where

equation becomes,

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!