Using the continuous exponential growth formula, N(t) = N0 × e^(rt), for a sample that started with 10 bacteria at a 5% hourly growth rate, there will be approximately 40 bacteria after 28 hours upon rounding down to the nearest whole number.
To calculate the number of bacteria after 28 hours when the sample began with 10 bacteria and is growing at an hourly rate of 5% with continuous exponential growth, we use the formula for continuous growth, N(t) = N0 × e^(rt), where N0 is the initial amount, r is the rate of growth, and t is the time in hours. Plugging in the values, we get N(28) = 10 × e^(0.05 × 28). After calculating the value, we round down to the nearest whole number.
Calculating this gives us N(28) = 10 × e^(1.4), which is approximately 10 × 4.0552 = 40.552. Therefore, after rounding down, the final number of bacteria after 28 hours is 40.