# How do you find the exponential growth function, if under ideal conditions, a population of rabbits has an exponential growth rate of 11.5% per day and it has an initial population of 900 rabbits?

Mar 2, 2016

Growth: y = a(1+r)^x ; y = 900(1+0.115)^x
where y is the population at time x, and x is the number of days.

#### Explanation:

Exponential functions are of the form $y = a \cdot {b}^{x}$
when a > 0 and the b is between 0 and 1, the function will be decreasing (decaying).
when a > 0 and the b is greater than 1, the function will be increasing (growing).

Any quantity that grows or decays by a fixed percent at regular intervals is said to possess exponential growth or exponential decay.
there are two functions that can be easily used to illustrate the concepts of growth or decay in applied situations. When a quantity grows by a fixed percent at regular intervals, the pattern can be represented by the functions:

Growth:$y = a {\left(1 + r\right)}^{x}$
Decay: $y = a {\left(1 - r\right)}^{x}$
WHERE:
a = initial amount before measuring growth/decay
r = growth/decay rate (often a percent)
x = number of time intervals that have passed
http://www.regentsprep.org/regents/math/algebra/ae7/expdecayl.htm