## 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

- 400000=120[14π(D2−10000)]

(…3 weeks 1 day ago - Use integration by parts for…1 month 2 weeks ago
- need answer1 month 2 weeks ago
- Yes you are absolutely right…1 month 3 weeks ago
- I think what is ask is the…1 month 3 weeks ago
- $\cos \theta = \dfrac{2}{…1 month 3 weeks ago
- Why did you use (1/SQ root 5…1 month 3 weeks ago
- How did you get the 300 000pi1 month 3 weeks ago
- It is not necessary to…1 month 3 weeks ago
- Draw a horizontal time line…1 month 4 weeks ago

## Re: Growth problems

$\dfrac{dP}{dt} = kP$

$\dfrac{dP}{P} = k \, dt$

$\displaystyle \int \dfrac{dP}{P} = k \int dt$

$\ln P = kt + C$

$\ln P = \ln e^{kt} + C$

$\ln P - \ln e^{kt} + C$

$C = \ln \dfrac{P}{e^{kt}}$

When t = 0, P = 2

$C = \ln \dfrac{2}{e^{0}}$

$C = \ln 2$

Hence,

$\ln 2 = \ln \dfrac{P}{e^{kt}}$

$2 = \dfrac{P}{e^{kt}}$

$P = 2e^{kt}$

When t = 2, P = 3

$3 = 2e^{2k}$

$\dfrac{3}{2} = e^{2k}$

$e^k = \left( \dfrac{3}{2} \right)^{1/2}$

Thus,

$P = 2\left( \dfrac{3}{2} \right)^{t/2}$

(a) for t = 1

$P = 2\left( \dfrac{3}{2} \right)^{1/2} = 2.4495 ~ \text{oz}$

answer(b) for t = 10

$P = 2\left( \dfrac{3}{2} \right)^{5} = 15.1875 ~ \text{oz}$

answer## Re: Growth problems: mold grows at a rate proportional to its...

post lang ako uli sir