In a lab experiment, 40 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 28 hours. How many bacteria would there be after 10 hours, to the nearest whole number? Answer:

Question

Bytelearn · Accepted Answer

Understand and Identify: Understand the problem and determine what is given and what needs to be found. We know: Initial number of bacteria: 40 Doubling time: 28 hours Time elapsed: 10 hours We need to find the number of bacteria after 10 hours.Calculate Doubling Periods: Calculate the number of times the bacteria population will double in 10 hours. Since the bacteria double every 28 hours, we need to find out how many 28-hour periods fit into 10 hours. However, since 10 hours is less than 28 hours, the bacteria will not have doubled even once in that time frame.Determine Growth Rate: Determine the growth rate per hour. To find the growth rate per hour, we assume exponential growth and use the formula for exponential growth: N = N0 * e^(kt), where N is the final amount, N0 is the initial amount, k is the growth rate, and t is the time in hours. Since we don't have a full doubling period, we need to solve for k using the doubling time. Doubling formula: N = N0 * 2^(t/T), where T is the doubling time. 2 = e^(k*28) k = ln(2) / 28Calculate Growth Rate: Calculate the growth rate k. k = ln(2) / 28 k ≈ 0.0248 (rounded to four decimal places)Use Growth Rate: Use the growth rate to calculate the number of bacteria after 10 hours. N = 40 * e^(0.0248*10) N ≈ 40 * e^(0.248)Evaluate Expression: Evaluate the expression to find the final number of bacteria. N ≈ 40 * e^(0.248) N ≈ 40 * 1.282 (using a calculator for e^(0.248)) N ≈ 51.28Round Final Result: Round the number of bacteria to the nearest whole number. The number of bacteria after 10 hours, rounded to the nearest whole number, is approximately 51.

In a lab experiment, $40$ bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every $28$ hours. How many bacteria would there be after $10$ hours, to the nearest whole number? $\newline$ Answer:

Full solution

More problems from Convert between customary and metric systems

Related topics

In a lab experiment, 404040 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 282828 hours. How many bacteria would there be after 101010 hours, to the nearest whole number?\newlineAnswer:

In a lab experiment, $40$ bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every $28$ hours. How many bacteria would there be after $10$ hours, to the nearest whole number? $\newline$ Answer: