Question

A research student is working with a culture of bacteria that doubles in size every fifteen minutes. The initial population count was 3 bacteria. Write an exponential equation representing this situation. Use t to represent hours. If you use the exponential function Poel, round your value for k to 4 decimal places. P(t) = It) Preview syntax error To the nearest whole number, what is the population size after 3 hours?

Answer 1

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.

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