Question

An insect population dies of exponentially and is governed by the equation p′=−µp, where µ is the mortality rate. If 1200 insects hatch, and only 70 remain after 6 days, what is the mortality rate?.

Answer 1

Answer:

$47.36\%$

Step-by-step explanation:

The equation that governs how the insect population dies is

$p' = - \mu p$

We need to solve this differential equation for p.

We separate variables to get:

$\frac{p'}{p} = - \mu$

We integrate both sides to get:

$\int\frac{p'}{p} dt = - \mu \int \: dt$

$ln( |p| ) = - \mu \: t + ln(k)$

$p = c{e}^{ \ - ut}$

If 1200 insects hatch, and only 70 remain after 6 days,

Then we have:

$70 = 1200 {e}^{ - 6 \mu}$

$\frac{70}{1200} = {e}^{ - 6 \mu}$

$- 6 \mu = ln( \frac{7}{120} )$

$\mu = \frac{ln( \frac{7}{120} ) }{ - 6}$

$\mu = 0.4736$

$47.36\%$