Question

bacteria in a culture increase at a rate that is proportional at any time to the number of bacteria at that time. there were 800 800800 bacteria initially, and they triple every 10 1010 hours. what is the number of bacteria after 4 44 hours? round to the nearest integer.

Answer 1

The number of bacteria after 4 hours is approximately 1,030.

Step-by-step explanation:

Bacteria in a culture increase at a rate that is proportional to the number of bacteria at that time. In this case, the bacteria triple every 10 hours. To calculate the number of bacteria after 4 hours, we can divide the total time (4 hours) by the doubling time (10 hours) to find the number of doublings that have occurred. In this case, 4 hours divided by 10 hours gives us 0.4 doublings. To find the number of bacteria after 4 hours, we multiply the initial number of bacteria (800) by 3 raised to the power of the number of doublings (0.4). This gives us approximately 1,030 bacteria after 4 hours.

Answer 2

The number of bacteria in the culture increases at a proportional rate and triples every 10 hours. To find the number of bacteria after 4 hours, we can use the formula for exponential growth. After performing the calculations and rounding to the nearest integer, the number of bacteria after 4 hours is approximately 1,674.

Step-by-step explanation:

The bacteria in the culture increase at a rate that is proportional to the number of bacteria at any given time. In this case, the bacteria triple every 10 hours. The initial number of bacteria is 800. To find the number of bacteria after 4 hours, we can use the formula for exponential growth:

`N = N0 * e^(kt)`

Where N is the final number of bacteria, N0 is the initial number of bacteria, k is the growth rate (ln(3)/10), and t is the time in hours.

Plugging in the values, we get:

`N = 800 * e^(ln(3)/10 * 4)`

`N = 800 * e^(4ln(3)/10)`

Simplifying further:

N ≈ 800 * 2.0926

N ≈ 1,674.08

Rounding to the nearest integer, the number of bacteria after 4 hours is approximately 1,674.