A population of protozoa develops with a constant relative growth rate of 0.7233 per member per day. On day zero the population
consists of four members. Find the population size after six days.
1 answer:
Answer:
307 members
Step-by-step explanation:
Relative growth rate= Growth rate/population
Given: constant relative growth rate=0.7233
0.7233=![\frac{dP/dt}{P}](https://tex.z-dn.net/?f=%5Cfrac%7BdP%2Fdt%7D%7BP%7D)
![\frac{dP}{dt} =0.7233 P](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%20%3D0.7233%20P)
Theorem 2 states that solutions of the differential equation dy/dt = ky are in the form: y(t)=y(0)![e^k^t](https://tex.z-dn.net/?f=e%5Ek%5Et)
Writing the soltuion of our dif. equation as:
P(t)=P(0)![e^{0.7233t}](https://tex.z-dn.net/?f=e%5E%7B0.7233t%7D)
since on day zero the population consists of four members.
P(t)=4![e^{0.7233t}](https://tex.z-dn.net/?f=e%5E%7B0.7233t%7D)
next is to find the population size after six days. i.e t=6
P(6)=4
≈ 307 members
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Step-by-step explanation:
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