Question

The population of Henderson City was 3,381,000 in 1994, and is growing at an annual rate 1.8%

Answer 1

In the year 2000, population will be 3,762,979 approximately. Population will double by the year 2033.

Step-by-step explanation:

   Given that the population grows every year at the same rate( 1.8% ), we can model the population similar to a compound Interest problem.

   From 1994, every subsequent year the new population is obtained by multiplying the previous years' population by $\frac{100+1.8}{100}$ = $\frac{101.8}{100}$.

   So, the population in the year t can be given by $P(t)=3,381,000\textrm{x}(\frac{101.8}{100})^{(t-1994)}$

   Population in the year 2000 = $3,381,000\textrm{x}(\frac{101.8}{100})^{6}$=$3,762,979.38$

Population in year 2000 = 3,762,979

   Let us assume population doubles by year $y$.

$2\textrm{x}(3,381,000)=(3,381,000)\textrm{x}(\frac{101.8}{100})^{(y-1994)}$

$log_{10}2=(y-1994)log_{10}(\frac{101.8}{100})$

$y-1994=\frac{log_{10}2}{log_{10}1.018}=38.8537$

$y$≈$2033$

∴ By 2033, the population doubles.