Final answer:
The growth constant, k, for the bacteria problem is calculated using the exponential growth formula and the known values of bacteria over a 10-hour period. With k found, the number of bacteria after 18 hours is determined by applying the exponential growth formula again with t set to 18 hours.
Step-by-step explanation:
To determine the growth constant, k, for the bacteria growth problem, we can use the formula for exponential growth: N(t)=N(0)e^(kt), where N(0) is the initial number of bacteria, N(t) is the number of bacteria after time t, and e is the base of the natural logarithm.
The growth constant can be found by solving for k when we know N(0)=70, N(10)=380, and t=10 hours. Rearranging the formula to solve for k, we get k = (1/t)ln(N(t)/N(0)). Substituting the known values, we find that k ≈ (1/10)ln(380/70).
After calculating k, we can then use the exponential growth formula again to find the number of bacteria after 18 hours, N(18), using N(0)=70, the calculated k, and t=18. Again, we use N(18)=N(0)e^(k*18) to get the answer.