Calculus 1 : Rate
Study concepts, example questions & explanations for Calculus 1
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Example Questions
Example Question #63 : How To Find Constant Of Proportionality Of Rate
The rate of change of the trout population in Lake Tahoe is proportional to the population. The population increased by 42 percent between January and April. What is the constant of proportionality in months-1?
We're told that the rate of growth 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 42 percent between January and April, we can solve for this constant of proportionality. Treat the months as their number in the calendar:
Example Question #64 : How To Find Constant Of Proportionality Of Rate
The rate of change of the the number of E. coli in room-temperature hamburger is proportional to the population. The population increased by 100 percent between 4:10 and 4:30. What is the constant of proportionality in seconds-1?
We're told that the rate of growth 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 100 percent between 4:10 and 4:30, we can solve for this constant of proportionality. Note that units we're asked to use:
Example Question #65 : How To Find Constant Of Proportionality Of Rate
The rate of change of the number of pike in Lake Mead is proportional to the population. The population increased by 48 percent between 2014 and 2015. What is the constant of proportionality in years-1?
We're told that the rate of growth 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 48 percent between 2014 and 2015, we can solve for this constant of proportionality:
Example Question #961 : Rate
The rate of growth of the population of wild foxes in Britain is proportional to the population. The population increased by 113 percent between 2011 and 2015. What is the constant of proportionality in years-1?
We're told that the rate of growth 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 113 percent between 2011 and 2015, we can solve for this constant of proportionality:
Example Question #61 : How To Find Constant Of Proportionality Of Rate
The rate of growth of the number of swallows in Saksegawa is proportional to the population. The population increased by 8 percent between 2013 and 2015. What is the constant of proportionality in years-1?
We're told that the rate of growth 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 8 percent between 2013 and 2015, we can solve for this constant of proportionality:
Example Question #2761 : Functions
The rate of growth of the number of belugas in the pacific is proportional to the population. The population increased by 148 percent between 2010 and 2015. What is the constant of proportionality in years-1?
We're told that the rate of growth 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 148 percent between 2010 and 2015, we can solve for this constant of proportionality:
Example Question #71 : How To Find Constant Of Proportionality Of Rate
The rate of decrease of the number of grey wolves is proportional to the population. The population decreased by 33 percent between 2008 and 2015. What is the constant of proportionality in years-1?
We're told that the rate of decrease 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 33 percent between 2008 and 2015, we can solve for this constant of proportionality:
Example Question #962 : Rate
The rate of decrease of the Siberian tiger population of northern Asia is proportional to the population. The population decreased by 18 percent between 2009 and 2015. What is the constant of proportionality in years-1?
We're told that the rate of decrease 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 18 percent between 2009 and 2015, we can solve for this constant of proportionality:
Example Question #2762 : Functions
The rate of decrease of the number of puffins is proportional to the population. The population decreased by 27 percent between 2003 and 2007. What is the constant of proportionality in years-1?
We're told that the rate of decrease 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 27 percent between 2003 and 2007, we can solve for this constant of proportionality:
Example Question #72 : How To Find Constant Of Proportionality Of Rate
The rate of growth of the numbers of sunflowers in Nevada is proportional to the population. The population increased from 11000 to 17000 between 2012 and 2015. What is the constant of proportionality in years-1?
We're told that the rate of growth 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 11000 to 17000 between 2012 and 2015, we can solve for this constant of proportionality:
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