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A forest has 800 pine trees, but a disease is introduced that kills a fourth of the pine trees in the forest
every year.
Which graph shows the number y of pine trees remaining in the forest 2 years after the disease is
introduced?
In a graph

Sagot :

The exponential function that models the number of trees after t years is given by:

[tex]A(t) = 800\left(\frac{3}{4}\right)^t[/tex]

Hence, after 2 years, 450 trees will be remaining, as the graph at the end of this answer shows.

What is an exponential function?

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

In this problem:

  • The forest has 800 pine trees, hence A(0) = 800.
  • Each year, a disease is introduced that kills a fourth of the pine trees in the forest every year, hence [tex]r = \frac{1}{4}[/tex].

Then, the equation is:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 800(1 - \frac{1}{4})^t[/tex]

[tex]A(t) = 800\left(\frac{3}{4}\right)^t[/tex]

After 2 years:

[tex]A(2) = 800\left(\frac{3}{4}\right)^2 = 450[/tex]

450 trees will be remaining.

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

View image Joaobezerra
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