Question

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

!
t days
2
4
estimated number of organisms, n
860
1,250
1,800
2,600
3,720
10
Which equation best models the situation?
{= 1.2(600)"
On=600(1.2)
n=1.2(600)
{= 600(1.2)"

Answer 1

The best model for the student's population growth scenario is an exponential equation, which involves a base number and exponent to account for the growth rate and the number of generations or time periods.

Step-by-step explanation:

The question revolves around finding the appropriate exponential growth equation that models the growth of a population over time, given a table with estimated numbers of organisms on specific days. To model exponential growth, we generally use the formula N = N0ekt where N is the population at time t, N0 is the initial population, k is the growth rate, and e is the base of the natural logarithm. In the case of doubling, the formula can be modified to N1 = No × 2n, where n denotes the number of generations or doubling periods that have occurred. For practical applications involving large numbers, such as a population reaching 3 times its original size, we use scientific notation or switch between various bases, such as b = 1.05 or b = 2, to represent the growth more conveniently.

Answer 2

n = 600(1.2)^t

Step-by-step explanation: