The rate of change in the number of bacteria in a culture is proportional to the number present. In a certain laboratory experiment, a culture has 10,000 bacterial initially, 20,000 bacteria at time t 1 minutes, and 100,000 bacteria at (t 1+10 ) minutes. a. In terms of t only, find the number of bacteria in the culture at any time t minutes, t ≥ 0b. How many bacteria were there after 20 minutes?c. How many minutes had elapsed when the 20,000 bacteria were observed?

(a)

(b) 25,000

(c) 4.3068 min.

Step-by-step explanation:

Rate of change in the number of bacteria is proportional to the number present.

Let N is the population of bacteria.

∝ N ⇒ { k = proportionality constant}

initial population No. = 10,000

                          = 20,000

         and

(a) For population growth

----------(1)

----------(2)

from equation (1) and (2)

so expression will be

(b) for t = 20

             =  

            = 10,000 × 25

            = 25,000

(c) Since   [from equation (1)]

                  = 4.3068

                 = 4.3068 min.

he spend 5.1 minutes chatting with his friends.

step-by-step explanation:

2/5+1/2=9/10

6/1-9/10=5.1