In t years after 2000 the
population will be P(t) = P0ekt. Given P(0) =
and P(10) = 14.3×106,
From the latter equation e10k
= 14.3/12.7 and
ln(14.3/12.7)/10 = 0.01187. The population grows according to the
exponential law as
2015 the population will be P(15) = 12.7×106
e0.01187×15= 15.2 million.
P(t) = 18×106,
then from the equation 18×106
e0.01187twe get e0.01187t
= 18/12.7 = 1.417. Take the natural logarithm of both sides: 0.01187
t = ln(1.417) and t = ln(1.417)/0.01187 = 29.4 years
The independent variable is the time (in years) that passed since 2000 and the dependent variable is the population size. The population size is changing according to the exponential law, that is, P(t) = P_0 times e^(kt), where P_0 and k are some constants that can be found if two corresponding values of t and P(t) are given. If t = 0, then e^0 = 1, so P(0) = P_0 is the initial population (in 2000).
The second pair t = 10 and P(10) = 14,300,000 was used to find the constant k. After both P_0 and k are found, it is possible to use the formula P(t) = P_0 times e^(kt) either to find P(t) for given t or to find t for given value of P(t).