Final answer:
The function y=590(1.061)^x represents exponential growth at a rate of 6.1% per year. The base of the exponent, 1.061, is greater than 1, which indicates an increase in value.
Step-by-step explanation:
The exponential function given in the question is y=590(1.061)^x. To identify whether the function represents exponential growth or decay, we look at the base of the exponent, which is 1.061. Since the base is greater than 1, it indicates that the function models exponential growth. To find the percentage rate of increase, we subtract 1 from the base of the exponent and multiply by 100.
Percentage rate of increase = (1.061 - 1) × 100 = 0.061 × 100 = 6.1%
Therefore, the function y=590(1.061)^x represents exponential growth at a rate of 6.1% per year.
For example, using this growth rate over a 10-year period, the function's value would increase considerably. To see this, we would calculate: y = 590 × (1.061)^10. After performing the calculations, we would find a significant increase in the value of y, confirming a steady exponential growth pattern.