Answer:
1.24 weeks
Step-by-step explanation:
The ant population a(t) can be modeled by ...
a(t) = 400·(700/400)^t . . . . . where t is in weeks
The population will have doubled when a(t) = 800, so we want to find t for ...
800 = 400·(7/4)^t
2 = (7/4)^t . . . . . . . . . . . divide by 400
log(2) = t·log(7/4) . . . . . take the log
t = log(2)/log(7/4) ≈ 1.2386 ≈ 1.24 . . . . . weeks
It took about 1.24 weeks for the population to double.
