Population and Year Data Used

The data used in for this project is as follows:

year <- c(0, 10, 20, 30, 40, 50, 60)
pop <- c(3.929, 5.308, 7.240, 9.638, 12.866, 17.069, 23.192)

It is important to note that the year 1790 is represented by 0 and 1850 by 60. The reason for this because using the actual years will cause significant issues for the purposes of this experiment.

Plotted Data with FitLine

## Loading required package: proto

The following figure depicts year versus population with a fit line for the data.

Equation Used for Fitline

The equation used for the fit line was as follows: \[ pop = pop(ini) * exp (k*year) \]

K Value and Intercept Found Using nls2

The summary from the fitline shows the k value as follows:

## 
## Formula: pop ~ pop_ini * exp(k * year)
## 
## Parameters:
##          Estimate Std. Error t value Pr(>|t|)    
## pop_ini 3.9744064  0.0407277   97.58 2.14e-09 ***
## k       0.0293421  0.0002023  145.02 2.96e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09817 on 5 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.027e-08

The intercept and code used is shown as follows:

##  pop_ini 
## 3.974406