Calculus 1 : Constant of Proportionality
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Example Questions
Example Question #3891 : Calculus
The rate of change of the gila mobsters in the lizard mafia is proportional to the population. The population increased from 2300 to 13200 between 2013 and 2015. What is the constant of proportionality in years-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 2300 to 13200 between 2013 and 2015, we can solve for this constant of proportionality:
Example Question #3891 : Calculus
The rate of change of the number of gila monsters is proportional to the population. The population increased from 1800 to 9000 between 2014 and 2015. What is the constant of proportionality in years-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 1800 to 9000 between 2014 and 2015, we can solve for this constant of proportionality:
Example Question #3893 : Calculus
The rate of change of the number of leaves on trees in fall is proportional to the population. The population decreased from 120000 to 1000 between October 18th and 22nd. 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 from 120000 to 1000 between October 18th and 22nd, we can solve for this constant of proportionality:
Example Question #3894 : Calculus
The rate of change of the number of chromatic dragons is proportional to the population. The population increased from 100 to 1700 between March 3rd and 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 increased from 100 to 1700 between March 3rd and 8th, we can solve for this constant of proportionality:
Example Question #171 : Constant Of Proportionality
The rate of change of the number of princes turned frogs is proportional to the population. The population increased from 10 to 3900 between 1564 and 1565. What is the constant of proportionality in years-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 10 to 3900 between 1564 and 1565, we can solve for this constant of proportionality:
Example Question #3896 : Calculus
The rate of change of the number of mold spores is proportional to the population. The population increased from 9 to 65610 between May 9th 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 9 to 65610 between May 9th and 13th, we can solve for this constant of proportionality:
Example Question #3897 : Calculus
The rate of change of the number of bacteria is proportional to the population. The population increased from 16 to 2560 between 3:15 and 3:25. What is the constant of proportionality in minutes-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 16 to 2560 between 3:15 and 3:25, we can solve for this constant of proportionality:
Example Question #3898 : Calculus
The rate of change of the number of witches' familiars is proportional to the population. The population increased from 10 to 300 between October 29th 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 10 to 300 between October 29th and 30th, we can solve for this constant of proportionality:
Example Question #3899 : Calculus
The rate of change of the number of black squirrels is proportional to the population. The population increased from 110 to 133100 between 2012 and 2015. What is the constant of proportionality in years-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 110 to 133100 between 2012 and 2015, we can solve for this constant of proportionality:
Example Question #3900 : Calculus
The rate of change of the number of flap-flaps is proportional to the population. The population increased from 1400 to 9800 between February and April. What is the constant of proportionality in months-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 1400 to 9800 between February and April, we can solve for this constant of proportionality (it would be useful to write the months by their place in the calendar):
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