Calculus 1 : How to find constant of proportionality of rate
Study concepts, example questions & explanations for Calculus 1
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Example Questions
Example Question #1041 : Rate
The rate of change of the number of spooky scary skeletons is proportional to the population. The population increased by 18900 percent between October 15th and October 31st. What is the constant of proportionality in days-1?
We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:
Where 
Since the population increased by 18900 percent between October 15th and October 31st, we can solve for this constant of proportionality:
Example Question #1042 : Rate
The rate of change of the number of vampires is proportional to the population. The population decreased by 97.5 percent between November 1st and November 8th. What is the constant of proportionality in days-1?
We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:
Where
Since the population decreased by 97.5 percent between November 1st and November 8th, we can solve for this constant of proportionality:
Example Question #1043 : Rate
The rate of change of the number of werewolves is proportional to the population. The population decreased by 5.3 percent between November 1st and 10th. What is the constant of proportionality in days-1?
We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:
Where
Since the population decreased by 5.3 percent between November 1st and 10th, we can solve for this constant of proportionality:
Example Question #151 : How To Find Constant Of Proportionality Of Rate
The rate of change of the number of zombies is proportional to the population. The population decreased by 52.5 percent between November 3rd and 6th. What is the constant of proportionality in days-1?
We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:
Where
Since the population decreased by 52.5 percent between November 3rd and 6th, we can solve for this constant of proportionality:
Example Question #1051 : Rate
The rate of change of the number of swamp things is proportional to the population. The population decreased by 99.93 percent between November 5th and 7th. What is the constant of proportionality in days-1?
We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:
Where
Since the population decreased by 99.93 percent between November 5th and 7th, we can solve for this constant of proportionality:
Example Question #1052 : Rate
The rate of change of the number of unspoiled pumpkins is proportional to the population. The population decreased by 88.4 percent between November 14th and 18th. What is the constant of proportionality in days-1?
We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:
Where
Since the population decreased by 88.4 percent between November 14th and 18th, we can solve for this constant of proportionality:
Example Question #1053 : Rate
The rate of change of the number of spooky ghosts is proportional to the population. The population decreased by 10.13 percent between November 1st and 2nd. What is the constant of proportionality in days-1?
We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:
Where
Since the population decreased by 10.13 percent between November 1st and 2nd, we can solve for this constant of proportionality:
Example Question #3871 : Calculus
The rate of change of the number of goblins is proportional to the population. The population increased from 120 to 2400 between October 10th and 13th. What is the constant of proportionality in days-1?
We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:
Where
Since the population increased from 120 to 2400 between October 10th and 13th, we can solve for this constant of proportionality:
Example Question #1055 : Rate
The rate of change of the number of witches is proportional to the population. The population increased from 14 to 4200 between October 9th and 11th. What is the constant of proportionality in days-1?
We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:
Where
Since the population increased from 14 to 4200 between October 9th and 11th, we can solve for this constant of proportionality:
Example Question #1056 : Rate
The rate of change of the number of spooky, scary skeletons is proportional to the population. The population increased from 13 to 13000 between October 25th and 30th. What is the constant of proportionality in days-1?
We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:
Where
Since the population increased from 13 to 13000 between October 25th and 30th, we can solve for this constant of proportionality:
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