The rate of increase in the number of ba...

The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given the number triples in 5 hrs., find how many bacteria will be present after 10 hours. Also find the time necessary for the number of bacteria to be 10 times the number of initial present. [Given `(log)_e3=1. 0986 ,\ e^(2. 1972)=9` ]

Text Solution

Verified by Experts

The correct Answer is:

9 times, `5 (log 10 )/(log 3) ` hours.

Topper's Solved these Questions

DIFFERENTIAL EQUATIONS
MODERN PUBLICATION|Exercise CHECK YOUR UNDERSTANDING|10 Videos
DIFFERENTIAL EQUATIONS
MODERN PUBLICATION|Exercise COMPETITION FILE|17 Videos
DIFFERENTIAL EQUATIONS
MODERN PUBLICATION|Exercise Exercise|4 Videos
DETERMINANTS
MODERN PUBLICATION|Exercise Chapter test 4|12 Videos
INTEGRALS
MODERN PUBLICATION|Exercise COMPETITION FILE|24 Videos

Similar Questions

Explore conceptually related problems

The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. If in 5 hrs the number triples, then in 10 hrs, the number of bacteria present is

The rate of increases of bacteria in a certain culture is proportional to the number present. If it doubles in 5 hr.then in 25 hr.its number would be

The rate of increase in the number of bacteriad in a certain bacteria culture is propotional to the number present at that time. After 2 hours there are 600 becteria and after 8 hours the count is 75000, then the initial population is

The rate of increase in the number of bacteria in a certain culture is propotional to the number present at that time. After 2 hours there are 600 bacteria and after 8 hours the count is 75000, then the population will be 200000 after

The rate of increase of the bacteria in a culture is proportional to the number of bacteria present and it is found that the number doubles in 6hours.Prove that the bacteria becomes xx at the end of 18 hours.

The number of bacteria in a certain culture doubles every hour.If there were 30 bacteria present in the culture originally,how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour?

In a certain culture of bacteria, the rate of increase is proportional to the number present. If it is found that the number doubles in 4 hours, find the number of times the bacteria are increased in 12 hours.

Bacteria increases at the rate proportional to the number of bacteria present. If the original number N doubles in 3 hours, find in how many hours the number of bacteria will by 4N ?

MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-Revision Exercise

The slope of the tangent at a point P(x, y) on a curve is (- (y+3)/(x+...
Text Solution
|
Find the equation of the curve passing through the point (0,pi/4) w...
Text Solution
|
Find the equation of a curve passing through the point (1, 1), given t...
Text Solution
|
The decay rate of radium at any time t is proportional to its mass ...
Text Solution
|
Solve : (dy)/(dx)= (2x+3y-4)^(2).
Text Solution
|
Solve: (dy)/(dx)+y=e^x
Text Solution
|
Solve the following differential equation: (x^2-1)(dy)/(dx)+2(x+2)y=2\...
Text Solution
|
Solve: (dy)/(dx) = (y ( x + 2y))/(x ( 2x + y)) ,y(1) = 2
Text Solution
|
Solve each of the following initial value problem: (y^4-2x^3y)dx+(x^4-...
Text Solution
|
Solve each of the following initial value problem: x(x^2+3y^2)dx+y(y^2...
Text Solution
|
Solve each of the following initial value problems: (dy)/(dx)+(2x)/...
Text Solution
|
If ye^(y) dx = (y^(3) + 2xe^(y))dy, y(0) = 1, then the value of x when...
Text Solution
|
Find the particular solution of the differential equation (1+e^(2x))dy...
Text Solution
|
Find the particular solution of the differential equation. (dy)/(dx...
Text Solution
|
Find the particular solutions of : (1+xy)y dx + (1-xy)x dy = 0, y(1)...
Text Solution
|
The rate of increase in the number of bacteria in a certain bacteri...
Text Solution
|
The population of a city increases at a rate proportional to the numbe...
Text Solution
|
Assume that the rate at which radioactive nuclei decay is proportioanl...
Text Solution
|
If the interest is compounded continuously at 6% per annum, how muc...
Text Solution
|
A thermometer reading 80^0F is taken outside. Five minutes later the ...
Text Solution
|