A population numbers 11,000 organisms initially and grows by 12.4% each year. Suppose P represents population and t represents the number of years of growth. An exponential model for the population can be written in the form
P=ab^t , where P=
P = 11000(1.124)^t
How did you get 1.124?
12.4% = .124
100% = 1
so if something increases by 12.4% we end up with
100$ + 12.4% = 112.4% = 1.124
In the given problem, the population, P, is represented by the equation P=ab^t, where a represents the initial population and b represents the growth rate.
In this case, the initial population is 11,000 organisms, so a=11,000.
The growth rate is 12.4% each year, which means that the population increases by 12.4% annually.
To express this growth rate as a decimal, we divide it by 100: 12.4% / 100 = 0.124.
So, the growth rate, b, is 1 + 0.124, because the population increases by the growth rate. Therefore, b = 1.124.
Substituting the values of a and b into our equation, we get:
P = 11,000 * (1.124)^t.
This is the exponential model for the population growth, where P represents the population and t represents the number of years of growth.