I don't understand

Question

One estimate of the population of the world on January 1,2005 is 6,486,915,022. The pop. is estimated to be increasing at the rate of 1.4% per year. At this rate, what will the population of the world be on January 1, 2024? A. 9,086,227,907 B. 7,395,083,125 C. 8,448,105,986 D. 8,212,434,418

Answer 1

Let,

     P= Population on January 1,2005 = 6,486,915,022

     Rate= 1.4% = 1.4/100 = 0.014

In a year the population will be, (P+0.014P) = P(1+0.014) = P*1.014.

The working formula for this problem is

P_n = P*(1.014)ⁿ

Where n= number of years = (2024-2005) = 19

So,

    P₁₉ = 6,486,915,022*(1.014)¹⁹

          = 6,486,915,022* 1.30233029

          = 8448105986.35077215

          = 8448105986 (round it off)

Hence, the correct answer is C. 8,448,105,986

Answer 2

A = a₀(r)^t

A = 6486915022(1.014)¹⁹

A ≈ 6486915022(1.30233029995)

A ≈ ?