You want to know about the population dynamics of the earthworms you plan to put into your compost bin. You get a shipment of 250 worms to put into your bin and you calculate that your bin size can support 2000 worms. The company tells you that they have a per capita birth rate of 0.6 and per capita death rate of 0.2. What will be the instantaneous rate of change in population size over time (include 3 decimal places)

ANSWER: The instantaneous rate change in population of the warm is 0.400 and it will take the worm 7.999yrs to fill the bin.

Explanations: instantaneous change rate of a population is the rate difference between the birth rates and death rate of that population.

STEP 1: FIND THE DAILY BIRTH INCREASE.

birth rate = 0.6

Population = 250

Number of days in a year = 365

Their Daly birth increase will be;

(0.6 ÷ 365) × 250 = 0.411

STEP2: FIND THE DAILY DEATH INCREASE;

Death rate = 0.2

Population = 250

Number of days in a year = 365

Their daily death increase will be;

(0.2 ÷ 365) × 250 = 0.137

STEP 3: THE CHANGE IN THEIR DAILY POPULATION:

daily birth - daily death

0.411 - 0.137 = 0.274

STEP4: FIND THE INSTANTENEOUS CHANGE RATE:

Daily change in population = 0.274

Number of days in a year = 365

Number of population = 250

(365 × 0.274) ÷ 250 = 0.400

Therefore the instantaneous rate of change in the worm population is 0.400

TO CALCULATE HOW LONG IT WILL TAKE THE BIN TO FILL

(0.400 × 2000) ÷ 0.274 = 2919.706 days

Which is 2919.796/365 = 7.999yrs.

Therefore it will take the bin 7.999 years for the worm to fill the bin

sorry, but you do not have posted the diagram.

igneous rocks which formed by the crystallization of magma at the surface of the earth called extrusive rocks. they are characterized by fine-grained textures because the rapid cooling at or near the surface did not provide enough time for large crystals to grow.