A population numbers 10,000 organisms initially and grows by $12.6 \%$ each year. Suppose $P$ represents population, and $t$ the number of years of growth. An exponential model for the population can be written in the form $P=a \cdot b^{t}$ where \[ P= \]

Step 1 ：Translate the problem into mathematical terms. The initial population (a) is 10,000 and the growth rate (b) is 1 + 12.6/100 = 1.126. The model can be written as P = a * b^t.

Step 2 ：Substitute the given values into the model. The exponential model for the population growth is \(P = 10000 \cdot (1.126)^t\).

Step 3 ：Final Answer: \(\boxed{P = 10000 \cdot (1.126)^t}\)