SOLUTION: A rabbit population of 500 was introduced in a certain county of Eagleville. Biologists observe that the population increases 25% each year. Complete the following: a. Identify a

Algebra ->  Proportions -> SOLUTION: A rabbit population of 500 was introduced in a certain county of Eagleville. Biologists observe that the population increases 25% each year. Complete the following: a. Identify a       Log On


   

Question 1202148: A rabbit population of 500 was introduced in a certain county of Eagleville. Biologists observe that the population increases 25% each year. Complete the following:
a. Identify a and b.
b. Write an exponential function that models the situation if the trend continues.
c. How many rabbits will be in Eagleville after 10 years?
Answer by ikleyn(52781) About Me  (Show Source):
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A rabbit population of 500 was introduced in a certain county of Eagleville.
Biologists observe that the population increases 25% each year. Complete the following:
a. Identify a and b.
b. Write an exponential function that models the situation if the trend continues.
c. How many rabbits will be in Eagleville after 10 years?
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They want you write an exponential function of the form

    R(n) = a%2Ab%5En,

where R(n) is the population of rabbits "n" years from today, n = 0, 1, 2, 3, . . . 


It is

    R(n) = 500%2A%281%2B0.25%29%5En = 500%2A1.25%5En,


Thus a = 500 is the starting (initial) population;  b = 1.25 is the base of the exponential function
(the yearly growth coefficient).


Aften 10 years, the population will be

    R(10) = 500%2A1.25%5E10 = use your calculator = 4656.612873 = 4657 (rounded).    ANSWER

Solved.