Question

7. a. A colony of bacteria grows according to the Malthusian growth model $\frac{dB}{dt} = 0.01 B$, $B(0) = 1000$, where $t$ is in min. Solve this differential equation and determine how long it takes for this population to double. b. Because it takes a short time to adjust to the new medium, a better model is given by $\frac{dB}{dt} = 0.01(1 - e^{-t}) B$, $B(0) = 1000$. Solve this differential equation. c. Compare the populations predicted at $t = 5$ and 60 min.

          7. a. A colony of bacteria grows according to the Malthusian growth model
$\frac{dB}{dt} = 0.01 B$, $B(0) = 1000$,
where $t$ is in min. Solve this differential equation and determine how long it takes for this population
to double.
b. Because it takes a short time to adjust to the new medium, a better model is given by
$\frac{dB}{dt} = 0.01(1 - e^{-t}) B$, $B(0) = 1000$.
Solve this differential equation.
c. Compare the populations predicted at $t = 5$ and 60 min.

7. a. A colony of bacteria grows according to the Malthusian growth model
(dB)/(dt) = 0.01 B, B(0) = 1000,
where t is in min. Solve this differential equation and determine how long it takes for this population
to double.
b. Because it takes a short time to adjust to the new medium, a better model is given by
(dB)/(dt) = 0.01(1 - e^-t) B, B(0) = 1000.
Solve this differential equation.
c. Compare the populations predicted at t = 5 and 60 min.

Added by Cynthia S.

Advanced Engineering Mathematics

Dennis G. Zill, Warren S. Wright 5th Edition

Chapter 1

Instant Answer

Solved by Expert Charles Machakwa

Step 1

To solve the differential equation dB = 0.01B dt, we can separate the variables and integrate both sides: ∫(1/B) dB = ∫0.01 dt ln|B| = 0.01t + C Taking the exponential of both sides, we get: |B| = e^(0.01t + C) Since B(0) = 1000, we can substitute this into Show more…

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This is first order differential equations this is all one question 7. a. A colony of bacteria grows according to the Malthusian growth model dB = 0.01 B, dt B(0) =1000, where t is in min. Solve this differential equation and determine how long it takes for this population to double. b. Because it takes a short time to adjust to the new medium, a better model is given by dB =0.01(1 - e-t) B dt B(0) =1000. Solve this differential equation. c. Compare the populations predicted at t = 5 and 60 min.