Final answer:
The number of bacteria in the culture increases at a proportional rate and triples every 10 hours. To find the number of bacteria after 4 hours, we can use the formula for exponential growth. After performing the calculations and rounding to the nearest integer, the number of bacteria after 4 hours is approximately 1,674.
Step-by-step explanation:
The bacteria in the culture increase at a rate that is proportional to the number of bacteria at any given time. In this case, the bacteria triple every 10 hours. The initial number of bacteria is 800. To find the number of bacteria after 4 hours, we can use the formula for exponential growth:

Where N is the final number of bacteria, N0 is the initial number of bacteria, k is the growth rate (ln(3)/10), and t is the time in hours.
Plugging in the values, we get:


Simplifying further:
N ≈ 800 * 2.0926
N ≈ 1,674.08
Rounding to the nearest integer, the number of bacteria after 4 hours is approximately 1,674.