According to experimental statistics, a certain type of bacteria reproduces such that its quantity increases by a factor of 2.4 on average every 3.5 hours. Suppose a test tube in the laboratory initially contains 1000 of this type of bacteria. According to an exponential function model, approximately how many hours later will the quantity of this bacteria reach about $4 \times 10^{10}$? (Note: $\log 2 \approx 0.3010$, $\log 3 \approx 0.4771$) (1) 63 hours (2) 70 hours (3) 77 hours (4) 84 hours (5) 91 hours
According to experimental statistics, a certain type of bacteria reproduces such that its quantity increases by a factor of 2.4 on average every 3.5 hours. Suppose a test tube in the laboratory initially contains 1000 of this type of bacteria. According to an exponential function model, approximately how many hours later will the quantity of this bacteria reach about $4 \times 10^{10}$? (Note: $\log 2 \approx 0.3010$, $\log 3 \approx 0.4771$)\\
(1) 63 hours\\
(2) 70 hours\\
(3) 77 hours\\
(4) 84 hours\\
(5) 91 hours