The constant 1.01 in the function f(t) = 170(1.01)^{30t} represents the rate of change of the quantity over time. Specifically, it reveals that the quantity is increasing by 1.01% every month. Here's a breakdown of what the constant signifies:
1. The number 1.01 is a multiplier that indicates a 1.01% increase in the quantity for each unit increase in time (t). This means that the quantity is growing at a compounded rate of 1.01% per month.
2. In the context of exponential growth, the constant 1.01 is the growth factor. It is multiplied by the initial quantity (170 in this case) to calculate the new quantity after each time period.
3. To understand the impact of the constant 1.01 on the rate of change, you can consider an example: If the initial quantity is 100, after one month it would become 100 1.01 = 101 (an increase of 1). After two months, it would be 101 1.01 = 102.01, and so on. This illustrates how the quantity is growing by 1.01% each month due to the constant 1.01.
Overall, the constant 1.01 in the function f(t) = 170(1.01)^{30t} indicates a consistent rate of increase of 1.01% per month for the quantity being measured.
