Final answer:
The formula for finding the number of bacteria present is given by P=P0(10)t. To find the time it takes for 15,000 bacteria to be present, we can plug in the values into the formula and solve for t. The approximate time it will take for 15,000 bacteria to be present is 1.74 hours.
Step-by-step explanation:
The formula for finding the number of bacteria present is given by P=P0(10)^t where P is the final population, P0 is the initial population, and t is the time measured in hours.
To find the time it takes for 15,000 bacteria to be present, we can plug in the values into the formula:
15,000 = 275(10)^t
Divide both sides of the equation by 275:
55 = (10)^t
To solve for t, we can take the logarithm of both sides of the equation.
log(55) = log((10)^t)
Using logarithm properties, we can bring the exponent down:
t * log(10) = log(55)
Since log(10) is equal to 1, we can simplify the equation:
t = log(55)
Using a calculator, we can find that t is approximately 1.74 hours.