mydata <- read.csv ("Finals.csv")
YearVect <- mydata$Years
YearVect
## [1] 0 10 20 30 40 50 60
PopVect <- mydata$Pop
PopVect
## [1] 3.929 5.308 7.240 9.638 12.866 17.069 23.192
\(Population= P_{0} \cdot e^{(k*t)}\)
Where:
Population is the population after time t
\(P_{0}\) is the inital population
e is Euler’s number
k is the rate of growth
t is the time in years
plot(YearVect, PopVect, xlab = 'Year from 1790 to 1850', ylab= 'US popluation growth in millions',
main = "US population growth from 1790 to 1850")
tryfit <- nls(PopVect ~ 3.929 * exp (k*YearVect), start= c(k = 0.1))
summary(tryfit)
##
## Formula: PopVect ~ 3.929 * exp(k * YearVect)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## k 2.956e-02 5.747e-05 514.4 3.64e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1002 on 6 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 6.62e-07
lines(PopVect,predict (tryfit))
cf <- coef(tryfit)
Intercept <- cf[1]
Intercept
## k
## 0.02955991