Question

The amount of algae in a bloom, P, can be modeled by the equation P = t^4 + 6t^3+ 7t^2 + 8t, where t is measured in weeks. During what interval of t will the population of algae be greater than 500?


(−∞, −6.759) ∪ (3.452, ∞)
(6.759, 3.452)
(0.3452, ∞)
(0, 3.452)

Answer 1

Answer:

C. (0.3452, ∞)

Step-by-step explanation:

Answer 2

The interval of t when the population of algae will be greater than 500 is (3.452, ∞)

What is an equation?

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

For given question,

The amount of algae in a bloom, P, can be modeled by the equation $P = t^4 + 6t^3+ 7t^2 + 8t$ where t is measured in weeks.

We need to find the find the interval of t will the population of algae be greater than 500

So, we get an inequality,

$\Rightarrow P > 500\\\\\Rightarrow t^4 + 6t^3+ 7t^2 + 8t > 500\\\\\Rightarrow t (t^3 + 6 t^2 + 7 t + 8) > 500\\\\\Rightarrow t [t [t (t + 6) + 7] + 8] > 500\\\\\Rightarrow t > 3.45~~and ~~t < -6.759$

But time is measured in weeks.

So, t will not have the values from the interval (−∞, −6.759)

Therefore, the interval of t when the population of algae will be greater than 500 is (3.452, ∞)

Learn more about inequality here:

https://brainly.com/question/11897796

#SPJ2