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In order to control an algae bloom in a lake, scientists introduce some treatment products. Once the treatment begins, the area covered by algae A, in square yards, is given by the equation, Time ,t , is measured in weeks

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@MarlonBruhhhh
0


  1. In the equation, what does the 240 tell us about the algae? What does the 1/3  tell us?
  2. Create a graph to represent  when  is 0, 1, 2, 3, and 4. Think carefully about how you choose the scale for the axes. If you get stuck, consider creating a table of values.
  3. About how many square yards will the algae cover after 2.5 weeks? Explain your reasoning.


Sangeetha Pulapaka
1


1.240, tells us the initial amount of algae in the lake, \frac{1}{3} tells us the common decay factor.

2.When t = 0, A\ =\ 240\ \cdot\left(\frac{1}{3}\right)^{^0}=\ 240

When t = 1, A\ =\ 240\ \cdot\left(\frac{1}{3}\right)^{^1}=\ 80

When t = 2, A\ =\ 240\ \cdot\left(\frac{1}{3}\right)^{^2}\approx26.66

When t = 3,  A\ =\ 240\ \cdot\left(\frac{1}{3}\right)^{^3}\ \approx8.89

When t= 4, A\ =\ 240\ \cdot\left(\frac{1}{3}\right)^{^4}\approx2.97  



3.Plugging in t = 2.5 in the equation gives us

A\ =\ 240\ \cdot\left(\frac{1}{3}\right)^{2.5}\approx15.4\ squareyards.

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