Final answer:
The exponential equation representing the bacterial growth is P(t) = 3 * 2^4t. After 3 hours, the population would be 12288 to the nearest whole number.
Step-by-step explanation:
The given information tells us that the bacteria population starts at 3 and doubles every 15 minutes. Doubling every 15 minutes is the same as doubling 4 times per hour (since there are 60 minutes in an hour), so the rate is 4 times per hour. An exponential growth formula generally has the structure P(t) = P0 * ekt, where P0 is the initial amount, k is the growth rate, t is the time, and P(t) is the amount after time t.
In this case, we can write the equation as P(t) = 3 * 24t.
To find the number of bacteria after 3 hours, we plug t = 3 into the equation we have: P(3) = 3 * 24*3, which yields P(3) = 3 * 212 = 12288. So, to the nearest whole number, the population size after 3 hours is 12288 bacteria.
Learn more about Exponential Growth