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Paul is gathering data about moss growth in a local forest. He measured an area of 11 square centimeters on one particular tree and will come back in 6 months to measure the growth of the moss. If the area covered by moss multiplies by one and a half times each month, approximately how much area will the moss cover when Paul returns?

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newyorkdaughter
If you so 11 * 1.5 * 1.5 * 1.5 * 1.5 * 1.5 * 1.5 you get approximately 125.2969cm squared

Answer:

The area that moss cover when Paul returns is:

              [tex]125.296875\ \text{square\ centimeters}[/tex]

Step-by-step explanation:

The initial area that is measured by Paul about moss growth in a local forest is:  11 square centimeters.

We know that the increase in the area covered by moss is increasing exponentially.

Since each month it is increasing by a fixed constant 1.5 times as it was the previous month.

Hence, the function which represents the area covered by moss in x months is:

     [tex]A(x)=11\times (1.5)^x[/tex]

We are asked to find the value of function when x=6

i.e.

[tex]A(x)=11\times 1.5\times 1.5\times 1.5\times 1.5\times 1.5\times 1.5\\\\\\A(x)=125.296875\ \text{square\ centimeters}[/tex]

            Hence, the answer is:

            [tex]125.296875\ \text{square\ centimeters}[/tex]

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