altitude = c(0, 1.7087, 3.4091, 5.2045, 10.0239, 19.2010,
           30.1161, 43.1627, 53.6129)
pressure = c(14.696, 11.022, 7.348, 4.8982, 1.4696, 
             0.14696, 0.014696, 0.00147, 0.000147)
air=data.frame(altitude, pressure)
#
# plot the data
plot(air$altitude, air$pressure, 
     main="Atmospheric Pressure",
     xlab="Altitude (miles)",
     ylab="Pressure (psi)")
# 
# take the log(y) but not of the x's 
air_fit = lm(log(air$pressure) ~ 
               air$altitude)
summary(air_fit)
# 
# isolating the factor 
factor = air_fit$coefficients["air$altitude"]
factor  
#
# determining the coefficient 
coeff = exp(air_fit$coefficients["(Intercept)"])
coeff
#
#displaying the equation 
factor = round(factor,4)
coeff = round(coeff,3)
fit_eq=paste("y=",coeff,"exp(",factor,"x)")
text(20,10,fit_eq)
#
#displaying the curve
curve(coeff*exp(factor*x),0,54, add=TRUE, col="blue")