Question

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?

Answer 1

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

Answer 2

The area that moss cover when Paul returns is:

`125.296875\ \text{square\ centimeters}`

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:

`A(x)=11* (1.5)^x`

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

i.e.

`A(x)=11* 1.5* 1.5* 1.5* 1.5* 1.5* 1.5\\\\\\A(x)=125.296875\ \text{square\ centimeters}`

Hence, the answer is:

`125.296875\ \text{square\ centimeters}`