Question

in 2000, an invasive plant species covered 0.2% of an island. for the 5 years that followed, the area covered by the plant tripled every year.
A student said "That means that about half of the island's area was covered by the plant in 2005!"

do you agree with his Statement? explain your reasoning.​

Answer 1

Answer:

The statement is correct

see the explanation

Step-by-step explanation:

we know that

The equation of a exponential growth function is equal to

$y=a(1+r)^x$

where

y  is the area covered by the plant in percentage

x is the time in years since 2000

r is the rate of change

a is the initial value

In this problem we have

$r=200\%=200/100=2$

$a=0.2\%$

substitute the values

$y=0.2(1+2)^x$

$y=0.2(3)^x$

In the year 2005

$x=2005-2000=5\ years$

substitute the value of x in the exponential function

$y=0.2(3)^5=48.6\%$

48.6% is about 50%

therefore

The statement is correct

Answer 2

Using an exponential function, it is found that the area covered in 5 years is of 48.6%, which is close to 50%, hence, the statement is correct.

Exponential function:

An exponential function is modeled by:

$y(t) = y(0)(1 + r)^t$

In which:

• y(0) is the initial value.

• 1 + r is the rate of change.

In this problem:

• Initially, it covered 0.2% of the island, hence $y(0) = 0.2$.

• If triples every year, hence $1 + r = 3$.

Then, the equation is:

$y(t) = 0.2(3)^t$

In five years, the area covered will be of:

$y(5) = 0.2(3)^5 = 48.6$

The area covered in 5 years is of 48.6%, which is close to 50%, hence, the statement is correct.

To learn more about exponential functions, you can take a look at https://brainly.com/question/25537936