The initial number of bacteria in a Petri dish is 2,300 and grows at a rate of 3% per hour. Which best approximates the number of bacteria in the dish after 8 hours?
1803
2914
2,324
0
You don't need a calculator for this one. You KNOW it can't be 0 or 1803 since it MUST be more than 2300. And for 8 hours it is unreasonable to think it will grow only by 24 so the answer must be B; i.e., 2914.
To find the number of bacteria in the dish after 8 hours, we can use the formula for exponential growth, which is given by:
N = N0 * (1 + r)^t
Where:
N is the final number of bacteria
N0 is the initial number of bacteria
r is the growth rate as a decimal
t is the time in hours
Let's plug in the given values into the formula:
N = 2,300 * (1 + 0.03)^8
Calculating this expression, we get:
N ≈ 2,300 * (1.03)^8
≈ 2,300 * (1.260924933)
Rounding to the nearest whole number, we get:
N ≈ 2,900
Therefore, the best approximation for the number of bacteria in the dish after 8 hours is 2,900.
So, the answer is B) 2,914.