Final answer:
To find out how many hours it will take for the ant population to reach 100 ants, we can use the formula for exponential growth. After solving the equation, we find that it will take approximately 24.49 hours for the population to reach 100 ants.
Step-by-step explanation:
To find out how many hours it will take for the ant population to reach 100 ants, we can use the formula for exponential growth. The formula is: P = P0 * (1 + r)^n, where P is the final population, P0 is the initial population, r is the growth rate as a decimal, and n is the number of time periods. In this case, P0 = 30, P = 100, and r = 4% = 0.04 per hour. We need to find the value of n. Rearranging the formula, we have 100 = 30 * (1 + 0.04)^n. Divide both sides by 30 to get (1 + 0.04)^n = 100/30 = 10/3. Take the logarithm of both sides and solve for n: n * log(1 + 0.04) = log(10/3). Divide both sides by log(1 + 0.04) to get n = log(10/3)/log(1 + 0.04). Using a calculator, we find n ≈ 24.49. Therefore, it will take approximately 24.49 hours for the population to reach 100 ants.