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
