Yes, this word problem is solvable using exponential functions.
To solve this problem, we need to use the formula for exponential growth:
P(t) = P0 * e^(rt)
where P(t) is the population after t hours, P0 is the initial population, r is the growth rate, and e is the mathematical constant approximately equal to 2.71828.
In this problem, we are given that the population doubles in size every 25 hours. This means that the growth rate is 1/25, since the population is multiplying by 2 each time.
We are also given that there are about 1.35 million infections every year. Since there are 365 days in a year, this means there are about 1.35 million/365 = 3699.18 infections per day.
We can now use this information to find the initial population:
P0 = 3699.18 / e^(1/25 * 24 * 365)
P0 ≈ 2135.05
So the initial population is about 2135.05 bacteria.
To find the population after one year, we can use the formula again:
P(365 * 24) = 2135.05 * e^(1/25 * 24 * 365)
P(365 * 24) ≈ 3.89 x 10^18
Therefore, there are approximately 3.89 x 10^18 bacteria present after one year.