Question

A culture of the bacterium rhodobacter sphaeroides initially has 22 bacteria and t hours later increases at a rate of 3.4657e0.1386t bacteria per hour. Find the population size after two hours. (Round your answer to the nearest integer.)

Answer 1

The population size of Rhodobacter sphaeroides after two hours is calculated using the exponential growth formula N(t) = N0 * e^(rt), with the given initial population and growth rate. The result is rounded to the nearest integer.

Step-by-step explanation:

The question involves calculating the bacterial population size after two hours, given an initial population and a growth rate that follows an exponential function. To find the population size after two hours, we need to use the exponential growth formula:

N(t) = N0 * e^(rt)

where N(t) is the population size at time t, N0 is the initial population size, e is the base of the natural logarithms, and r is the growth rate.

For Rhodobacter sphaeroides, we have the initial population N0 = 22 bacteria, a growth rate of r = 0.1386 per hour, and t = 2 hours. Plugging these values into the formula, we get:

N(2) = 22 * e^(0.1386*2)

Calculating the exponential term e^(0.1386*2) and multiplying by 22, we find the population size after two hours. To get the answer as an integer, round the result to the nearest whole number.