Question 1t A bacterial culture starts with 500 bacteria and dombles in size every half-hour. 1. How many bacteria are there ofter 4 hours? II. How maly hacteria are there after $t$ hours? III. How many bacteria are there after 50 minutes?

Step 1 ：Convert 4 hours to minutes: 4 * 60 = 240 minutes.

Step 2 ：Calculate the number of half-hour intervals in 240 minutes: 240/30 = 8 intervals.

Step 3 ：Calculate the number of bacteria after 8 doubling intervals: 500 * 2^8 = 500 * 256 = 128000.

Step 4 ：Convert t hours to minutes: t * 60 minutes.

Step 5 ：Calculate the number of half-hour intervals in t * 60 minutes: (t * 60)/30 = 2t intervals.

Step 6 ：Calculate the number of bacteria after 2t doubling intervals: 500 * 2^(2t).

Step 7 ：Calculate the number of half-hour intervals in 50 minutes: 50/30 = 1.6667 intervals.

Step 8 ：Find the closest integer number of intervals: 1 interval.

Step 9 ：Calculate the number of bacteria after 1 doubling interval: 500 * 2^1 = 500 * 2 = 1000.