## Active forum topics

- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Eliminate the Arbitrary Constants
- Law of cosines
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Integration of 4x^2/csc^3x√sinxcosx dx
- application of minima and maxima
- Sight Distance of Vertical Parabolic Curve
- Application of Differential Equation: Newton's Law of Cooling

## New forum topics

- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Integration of 4x^2/csc^3x√sinxcosx dx
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Newton's Law of Cooling
- Law of cosines
- Can you help me po to solve this?
- Eliminate the Arbitrary Constants
- Required diameter of solid shaft

## Recent comments

- Use integration by parts for…1 week 6 days ago
- need answer1 week 6 days ago
- Yes you are absolutely right…2 weeks 2 days ago
- I think what is ask is the…2 weeks 2 days ago
- $\cos \theta = \dfrac{2}{…2 weeks 3 days ago
- Why did you use (1/SQ root 5…2 weeks 3 days ago
- How did you get the 300 000pi2 weeks 3 days ago
- It is not necessary to…2 weeks 4 days ago
- Draw a horizontal time line…3 weeks ago
- Mali po ang equation mo…4 weeks 2 days ago

## Differential Equation:

Differential Equation: Application of D.E.: Population GrowthA bacterial population

Bis known to have a rate of growth proportional to (B+ 25). Between noon and 2PM the population increases to 3000 and between 2PM and 3PM the population is increased by 1000 in culture. (a) Find an expression for the bacterial populationBas a function of time. (b) What is the initial bacterial population in the culture? (c) What is the total bacterial population in the culture at 4:15PM?## $\dfrac{dB}{dt} = k(B + 25)$

$\dfrac{dB}{dt} = k(B + 25)$

$\dfrac{dB}{B + 25} = k \, dt$

$\displaystyle \int \dfrac{dB}{B + 25} = k \int dt$

$\ln (B + 25) = kt + C$

At 2:00PM,

t= 2 andB= 3000$\ln 3025 = 2k + C$ ← eq. (1)

At 3:00PM,

t= 3 andB= 4000$\ln 4025 = 3k + C$ ← eq. (2)

From eq. (1) and eq. (2)

$k = 0.2856$

$C = 7.4434$

Hence,

$\ln (B + 25) = 0.2856t + 7.4434$ answer for (a)

At noon,

t= 0$\ln (B + 25) = 7.4434$

$B = 1683$ answer for (b)

At 4:15PM,

t= 4.25$\ln (B + 25) = 0.2856(4.25) + 7.4434$

$B = 5726$ answer for (c)

## Another solution (By

Another solution (By Calculator - CASIO fx-991ES PLUS):MODE 3 5

AC

$B + 25 = 0\hat{y}$

$B + 25 = 1708$

$B = 1683$ answer for (b)

$B + 25 = 4.25\hat{y}$

$B + 25 = 5751$

$B = 5726$ answer for (c)

Note:

$\hat{y}$ = SHIFT 1 5 5