How do you write an exponential function to model each situation & solve given the population of Warren Michigan was 145,600 in 1990. If the population decreases by 1.2% each year, predict the population in 1999?

Nov 23, 2016

Population in 1999 will be $130609$

Explanation:

As the present population is $145 , 600$ in 1990

As population decreases by 1.2% i.e. by a factor of $\frac{1.2}{100} = 0.012$,

population in 1991, one year after will be $145 , 600 \left(1 - 0.012\right)$

and in 1992, it will be $145 , 600 \left(1 - 0.012\right) \left(1 - 0.012\right) = 145 , 600 {\left(1 - 0.012\right)}^{2}$

or $145 , 600 \times {0.988}^{2}$

and this in 1999, it will be $145 , 600 \times {0.988}^{9} = 145 , 600 \times 0.8970414 = 130609$