A study was done on the population of a certain species of birds in a park. Suppose the population size, \( P(t) \), after \( t \) years is given by the following exponential function: \[ P(t)=623(1.13)^{t} \] Answer the following questions. What is the initial population size? [Select] Does the function represent growth or decay? [Select] By what percentage does the population size change yearly? [Select ]

The initial population size is represented by the constant in the function when \( t = 0 \), which is \( P(0) = 623(1.13)^{0} = 623 \). So, the initial population size is 623 birds. The function represents growth because the base of the exponent, 1.13, is greater than 1, indicating an increase in the population over time. The percentage change in population size yearly is calculated by taking the growth factor minus 1, so \( (1.13 - 1) \times 100 = 13\% \). Therefore, the population size increases by 13% each year!