An experiment starts and the population of a bacteria culture increases by 10% in the first hour. Assume that the population increases at a rate proportional to the amount of bacteria.
a) What is the doubling time?
b) If the initial population is 2,000, what is the population in 6 hours?

a) The doubling time is 7.27 hours.

b) The population is 6 hours will be 3,543.

Step-by-step explanation:

The population of the bacteria is modeled by the following equation:

In which P(0) is the initial population, P(t) is the population after t hours and r is the growth rate.

An experiment starts and the population of a bacteria culture increases by 10% in the first hour.

This means that

Which helps us find r.

So

Applying ln to both sides

So

a) What is the doubling time?

This is t when

So

Applying ln to both sides

The doubling time is 7.27 hours.

b) If the initial population is 2,000, what is the population in 6 hours?

This is P(6) when . So

The population is 6 hours will be 3,543.

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.

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step-by-step explanation: