Question

The estimated number of organisms in a population after t days is shown in the table below.

t days
estimated number of organisms, n
2
860
4
1,250
6
1,800
8
2,600
10
3,720

Which equation best models the situation?
t=1.2(600)^n
n=600(1.5)^t
n=1.2(600)^t
t=600(1.2)^n

Answer 1

Compute the daily growth factor: ratios for 2-day intervals ≈ 1250/860 ≈ 1.44, 1800/1250 = 1.44, 2600/1800 ≈ 1.444, 3720/2600 ≈ 1.431 → about 1.44 per 2 days. The per-day factor is √1.44 = 1.2. Solve for the initial amount A using t=2: 860 = A(1.2)^2 ⇒ A ≈ 860/1.44 ≈ 600.

So the best model is n = 600(1.2)^t, which fits the table (e.g. t=10 gives ≈3720).