Final answer:
The function for the total number of bacteria after x days starting with 1 bacterium and tripling each day is f(x) = 3^x. It shows exponential growth, with the number of bacteria increasing at a rapidly accelerating rate.
Step-by-step explanation:
The function that represents the total number of bacteria after x days when you start with 1 bacterium and triple the number every day is an exponential function. This function is represented as f(x) = 3^x.
On day 0, you start with 1 bacterium, so f(0) = 3^0 = 1. On day 1, the number triples to f(1) = 3^1 = 3 bacteria, and this pattern continues such that on day 2 you have f(2) = 3^2 = 9 bacteria, and so on.
Each day, the number of bacteria is tripled from the previous day's total, which is reflected in the exponent x of the base 3 in the function.
Exponential growth like this is characterized by a consistent rate of growth in which the number of bacteria increases at an accelerating rate.