Final answer:
Using the exponential growth model formula, the initial population and growth rate can be calculated from the provided population counts at different times. Once those constants are determined, a general expression for population after t hours can be established.
Step-by-step explanation:
To solve for the initial population of bacteria and an expression for the population after t hours, given the constant relative growth rate, we can use the formula for exponential growth, N(t) = N_0 * e^(rt), where N(t) is the population at time t, N_0 is the initial population, r is the growth rate, and e is the base of the natural logarithm.
Given that after 2 hours the population is 600, this can be represented as N(2) = N_0 * e^(2r) = 600. After 8 hours, the population is 75,000, so N(8) = N_0 * e^(8r) = 75,000. Dividing these two equations gives us e^(6r) = 125. From this, we can solve for r using logarithms and then solve for N_0. Once N_0 and r are found, we can substitute them back into the equation to find the general expression for N(t).