Option (2), n=600(1.2)^t is the correct answer that satisfies the given condition.
What is an equation?
"In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value. The most basic and common algebraic equations in math consist of one or more variables".
For the given situation,
The table shows the estimated number of organisms n in a population after t days.
For 2 days, the number of organisms is 860.
For 4 days, the number of organisms is 1250.
For 6 days, the number of organisms is 1791.
For 8 days, the number of organisms is 2579.
For 10 days, the number of organisms is 3720.
From the data provided,
t values are less and n values are the maximum values. So options (1) and (4) are incorrect.
We need to check options (2) and (3).
Option (2):
[tex]n=600(1.2^{t} )[/tex]
Consider t=2 and n=860
⇒ [tex]860=600(1.2^{2} )[/tex]
⇒ [tex]860[/tex] ≈ [tex]864[/tex]
Option (3):
[tex]n=1.2(600^{t} )[/tex]
Consider t=2 and n=860
⇒ [tex]860=1.2(600^{2} )[/tex]
⇒ [tex]860= 432000[/tex]
This is not equal.
Hence we can conclude that option (2), n=600(1.2)^t is the correct answer that satisfies the given condition.
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