Question

Yellow star thistle is an invasive plant species; it is a big threat in the Santa Monica Mountains national recreation area. Ecologists have gathered data to model the spreading of the plant. Suppose the land area (in square miles) has been overtaken by the thistle t years after 2000 is given by:

w(t) = 0.792t^3-4.196t^2 +3.872t +24.021.

1) 2000 to 2005 = ________

Answer 1

Using the numerical value of a function, the land area that has been overtaken by the thistle between 2000 and 2005 is of 13.460 square miles.

------------------

The numerical value of a function f(x) at $x = a$ if f(a).

------------------

In t years after 2000, the land area overtaken by thistle is:

$w(t) = 0.792t^3 - 4.196t^2 + 3.872t + 24.021$

------------------

The area between 2000 and 2005 is:

$w(2005 - 2000) - w(2000 - 2000) = w(5) - w(0)$

------------------

The numerical values are:

• $w(5) = 0.792(5)^3 - 4.196(5)^2 + 3.872(5) + 24.021 = 37.481$
• $w(0) = 0.792(0)^3 - 4.196(0)^2 + 3.872(0) + 24.021 = 24.021$
• $w(5) - w(0) = 37.481 - 24.021 = 13.460$

The land area overtaken by thistle between 2000 and 2005 is of 13.460 square miles.

A similar problem is given at https://brainly.com/question/23214987