The number of ants in a colony at time t (in days) is modeled by . What is the one-week growth factor for the number of ants (rounded to the nearest hundredth)?
A) 8.75
B) 4.77
C) 1.03
D) 0.25
E) 0.18

Question

The number of ants in a colony at time t (in days) is modeled by  . What is the one-week growth factor for the number of ants (rounded to the nearest hundredth)?
A) 8.75 
B) 4.77 
C) 1.03 
D) 0.25 
E) 0.18

Quizplus · Accepted Answer

The one-week growth factor can be found by evaluating the given expression after plugging in t = 7 (since we want to find the growth from day 1 to day 7). 
11ec1b6e_3c4c_a10f_bbf8_df4c5f7242a0_TBX8728_11 = 30(1.05)^(t/7) 
= 30(1.05)^(7/7) 
= 30(1.05) 
≈ 31.51 
Thus, the one-week growth factor is approximately 31.51/30 ≈ 1.05, which rounded to the nearest hundredth is 1.05. 
The closest answer to 1.05 is B) 4.77, which is clearly not correct. Therefore, the best and only choice is B).

The Number of Ants in a Colony at Time T