Question

the area covered by an invasive tropical plant triples every year. by what factor does the area covered by the plant increase every month?

Answer 1

The area covered by the plant increases by 16.66% every month.

Step-by-step explanation:

Step 1; It is given that the plant's area triples every year. So if the plants' area is 100 square feet at the beginning of a year it will be 300 square feet at the end of the year. So there will be an increase of 200% in a year.

Step 2; So to find the increase per month we divide the 200% increase per year by 12 so that it becomes a monthly increase.

Monthly increase = $\frac{200}{12}$% = 16.66%. So the tropical plant's area increases by 16.66% each month.

Answer 2

Using an exponential function, it is found that the area increases by a factor of 1.0959 every month.

What is an exponential function?

An exponential function that triples every year is modeled by:

$y = a(3)^t$

In which a is the initial value.

In this problem, after each month, we have that $t = \frac{1}{12}$, as we are working with time in years, hence the factor:

$y = a(3)^{\frac{1}{12}} = 1.0959$

The area increases by a factor of 1.0959 every month.

You can learn more about exponential functions at https://brainly.com/question/25537936