Question

youre studying the growth of a specific algae species in a pond for an environmental science project. the algaes coverage area is increasing each day at a consistent rate due to favorable conditions. the algae currently cover 100 square meters of the pond. let m be the daily growth rate of the algae. write and solve a linear inequality to find the maximum daily growth rate to prevent the algae from covering more than half of the 1,000 square - meter pond within the next 30 days. round your answer to the nearest tenth, if necessary. use the keypad to enter your answers in the boxes. additional symbols can be found using the drop - down arrow at the top of the keypad. an inequality that represents the situation is . the maximum daily growth rate of the algae that will prevent the algae from covering more than half the pond is square meters per day.

Explanation:

Step1: Set up the inequality

The initial coverage is 100 square - meters and it grows at a rate of $m$ square meters per day for 30 days. We want it to be less than or equal to half of the 1000 - square - meter pond (which is 500 square meters). So the inequality is $100+30m\leqslant500$.

Step2: Solve the inequality for $m$

Subtract 100 from both sides: $30m\leqslant500 - 100$, so $30m\leqslant400$.

Step3: Isolate $m$

Divide both sides by 30: $m\leqslant\frac{400}{30}=\frac{40}{3}\approx13.3$.

Answer:

An inequality that represents the situation is $100 + 30m\leqslant500$.
The maximum daily growth rate of the algae that will prevent the algae from covering more than half the pond is $13.3$ square meters per day.