a population doubles every month

Question

a-initial population 20, what is function that represents poulation with respect to time
b-how many present after 1 year and 5 years
c-when will there be 10,000

Answer 1

a) number = 20 (2)^(t) , where t is in months

b) in 1 year , t = 12
number = 20(2^12) = 81920
in 5 years , t = 60
number = 20(2^60) = 2.306 x 10^19 , ridiculous answer !

c) 20(2^t) = 10000
2^t = 500
ln both sides
tln2 = ln500
t = ln500/ln2 = 8.965 monts or appr 9 months

Answer 2

after m months,

p = 20*2^m

plug in values for m and evaluate
solve 20*2^m = 10000: m=8.