(3.452, ∞) is the interval of t whenever the population of algae would be greater than 500.
"It is an arithmetical statement consisting of two algebraic expressions with equal symbols."
Regarding the given question,
The equation can be used to model the quantity of algae in a bloom, P, where 't' is evaluated in weeks.
P = t⁴ + 6t³ + 7t² + 8t
We must determine the interval of t at which the population of algae will be greater than 500.
As a result, we have an inequality.
P > 500
t⁴ + 6t³ + 7t² + 8t > 500
taking 't' common.
t(t³ + 6t² + 7t + 8) > 500
This can be simplified as;
t[t(t + 6) + 7] + 8] > 500
t > 3.45 and t < - 6.759
However, time is expressed in weeks.
As a result, it will not contain values from of the interval (-∞,- 6.759).
As a result, the interval of t whenever the algae population would be higher than 500 is (3.452,∞ ).
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