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population of 895 quail increases at an annual rate of 17

by Skyler
(Tennessee)











































An initail population of 895 quail increases at an annual rate of 17. Write an exponential function to model the quail population.

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Dec 14, 2010
Exponential Growth Function
by: Staff

The question:


by Skyler
(Tennessee)


An initial population of 895 quail increases at an annual rate of 17.

Write an exponential function to model the quail population.



The answer:

The general form of an exponential growth function is:

V = ab^t

V = value of function
a = initial quantity
b = growth factor
t = time

In addition, b, the growth factor = 1+g
g = growth in 1 time period

The final equation can be written as:

V = a(1 + g)^t

When we apply this to your quail problem:

V = calculated number of quail
a = initial number of quail = 895 quail
g = 17% increase per year (converted to decimal, g = 0.17)
t = time in years

The equation for the growth of the quail population is:

V = a(1 + g)^t
V = 895(1 + .17)^t
V = 895(1.17)^t

The final answer is: V = 895(1.17)^t
(remember t = time in YEARS)




Thanks for writing.


Staff
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