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