an initial population of 865 quail increases at a annual rate of 15%. write an exponential function to model quail population
Pop(t) = 865 (1.15)^t , where t is the number of years
To write an exponential function to model the quail population, we need to consider the annual rate of growth. In this case, the population increases at a rate of 15% per year.
The general form of an exponential function is given by:
y = a * (1 + r)^t
Where:
- y represents the population after a certain number of years.
- a is the initial population (865 in this case).
- r is the growth rate expressed as a decimal (15% = 0.15 in this case).
- t is the number of years.
So, the exponential function to model the quail population in this situation would be:
y = 865 * (1 + 0.15)^t
Simplifying further, the exponential function would be:
y = 865 * (1.15)^t
This function represents how the quail population grows exponentially over time with an annual growth rate of 15%.