Question 192107
A=P(1+r)^t

1)   A(1) = 100(1.08)^1= 108
2)  A(2)=  100(1.08)^2=116.64
3) A(3)= 100(1.08)^3=125.97
4) A(n)=100(1.08)^n
5)  200=100(1.08)^n
divide  both  sides  by  100
2=(1.08)^n

log  both  sides

log2 =log (1.08)^n=n*log(1.08)

divide  both  sides  by  log(1.08)  and  simplify

(log(2))/(log(1.08))= 9.006=n

check
200=100log(1.08)^9.006=  200     ok