Since the population doubles every 44 hours, it can be modeled using an exponential equation as follows:
[tex]P(t)=405,000\times2^{\frac{t}{44}}[/tex]Where t is the time since the population was 405,000 measured in hours.
Replace t=176 to find the population after 176 hours:
[tex]\begin{gathered} P(176)=405,000\times2^{\frac{176}{44}} \\ =405,000\times2^4 \\ =405,000\times16 \\ =6,480,000 \end{gathered}[/tex]Therefore, the population after 176 hours will be 6,480,000
