Final answer:
The initial amount in the function y=34,400(.983)^x is 34,400, and the rate of decrease is calculated to be 1.7%.
Step-by-step explanation:
The equation you provided, y=34,400(.983)^x, is an exponential decay function. In such functions, the initial number is the value of y when x is 0.
Setting x to 0 in this function, we get y as 34,400, which indicates that the initial amount is 34,400. The rate of decrease is determined by the base of the exponent, 0.983 in this case.
To find this rate, we subtract it from 1 and multiply by 100 to get the percentage. Therefore, the rate of decrease is (1 - 0.983) × 100% = 1.7%.