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?

The area that moss cover when Paul returns is:

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:

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

i.e.

            Hence, the answer is:

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)