Question

A population of 752,000 people decreases at a rate of 1.4% each year. Let t represent the number of years and A(t) represent the amount after years, Which function models this situation?

Answer 1

Initial population, P = 752,000 .

Rate of decrease, r = 1.4 % .

Now, population decrease in 1st year :

`P_1 = P( 1 - 0.014 )`

Also, population decrease in 2nd year :

`P_2 = P_1( 1 -0.014 )\\\\P_2 = P( 1 - 0.014)^2`

Similarly for each next x year, population will be :

`P_x = P( 1-0.014)^x`

Therefore, population after x years is given by :

`P_x = 752000 ( 1-0.014)^x`