Final answer:
The function represents exponential growth with a constant percentage rate of 200%. The base of the exponent, 3, indicates the quantity triples per each time unit. The rule of 70 gives an estimate of doubling time but is less accurate for rates over 10%.
Step-by-step explanation:
The function f(t) = 246 x 3t represents exponential growth because the base of the exponent (3) is greater than 1. The rate of growth increases over time in a consistent percentage. To determine the constant percentage rate of growth, we look at the base of the exponent. Since the base is 3, this implies that the quantity is tripling with each unit increase in time. This triple rate, expressed as a percentage, is 200% growth per time unit because it is growing from 1x to 3x. Hence, the constant percentage rate is 200%.
Using the rule of 70, which is a quick formula to estimate the doubling time of an investment or in this case a function's growth, we would say that the time it takes for the function to double is approximately 70 divided by the percentage growth rate. However, since our rate is larger than 10% the rule is less accurate, yet it still gives a useful rough estimate.
In terms of calculations, we can say that exponential growth functions have the form P = P0ert, where P is the population at time t, P0 is the initial population, r is the growth rate, and t is time. The base 'e' represents the natural logarithm base, approximately equal to 2.71828.