Question

A culture of bacteria has an initial population of 94000 bacteria and doubles every 6 hours. using the formula p, start subscript, t, end subscript, equals, p, start subscript, 0, end subscript, dot, 2, start superscript, start fraction, t, divided by, d, end fraction, end superscriptp t ​ =p 0 ​ ⋅2 d t ​ , where p, start subscript, t, end subscriptp t ​ is the population after t hours, p, start subscript, 0, end subscriptp 0 ​ is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 19 hours, to the nearest whole number?

Answer 1

The population of bacteria after 19 hours, with an initial population of 94,000 and doubling every 6 hours, is approximately 873,036 to the nearest whole number.

Step-by-step explanation:

To calculate the population of bacteria after 19 hours when it doubles every 6 hours with an initial population of 94,000, we can use the formula pt = p0 · 2t/d, where:

• pt is the population after t hours,
• p0 is the initial population,
• t is the total time in hours,
• d is the doubling time in hours.

Given values are p0 = 94,000, t = 19 hours, and d = 6 hours. Plugging the values into the formula:

pt = 94000 · 219/6

First, calculate 19 divided by 6, which equals approximately 3.1667. Then raise 2 to the power of 3.1667:

23.1667 ≈ 9.2857

Now, multiply the initial population by this value:

pt = 94000 × 9.2857 ≈ 873,035.8

To the nearest whole number, the population after 19 hours is approximately 873,036 bacteria.

Answer 2

The population of bacteria in the culture after 19 hours is approximately 1,004,097.

To find the population of bacteria after 19 hours, we can use the given formula:

p subscript t = p subscript 0 * 2^(t/d)

Where:
- p subscript t is the population after t hours
- p subscript 0 is the initial population
- t is the time in hours
- d is the doubling time

In this case, the initial population p subscript 0 is 94000, the time t is 19 hours, and the doubling time d is 6 hours.

Now let's substitute these values into the formula:

p subscript 19 = 94000 * 2^(19/6)

To simplify the calculation, we can use a calculator or a spreadsheet software. After evaluating the expression, we find that the population of bacteria after 19 hours is approximately 1,004,097 (rounded to the nearest whole number).