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A wildlife refuge has 200 birds when it is first established. It is so
successful that the number of birds increases by 25% every year.
Write a function to model the situation.
Find the number of birds present after 7 years.

Respuesta :

MrRoyal

Answer:

[tex](a)\ f(x) =200(1.25)^x[/tex]

(b) 954 birds after 7 years

Step-by-step explanation:

Given

[tex]a = 200[/tex] --- initial

[tex]r =25\%[/tex] --- rate

Solving (a): The function.

This is represented as:

[tex]f(x) =a(1+r)^x[/tex]

So, we have:

[tex]f(x) =200(1+25\%)^x[/tex]

Express percentage as decimal

[tex]f(x) =200(1+0.25)^x[/tex]

[tex]f(x) =200(1.25)^x[/tex]

Solving (b): Birds after 7 years

This implies that we calculate f(7)

[tex]f(7) =200(1.25)^7[/tex]

[tex]f(7) =953.67[/tex]

[tex]f(7) =954[/tex] --- approximated

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