Calculus 1 : Calculus
Study concepts, example questions & explanations for Calculus 1
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Example Questions
Example Question #3831 : Calculus
The rate of growth of the number of trash-hungry pigeons is proportional to the population. The population increased from 1300 to 28,600 between 2010 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 1300 to 28,600 between 2010 and 2015, we can solve for this constant of proportionality:
Example Question #3832 : Calculus
The rate of growth of the number of pinethrushes in Beulica is proportional to the population. The population increased from 5400 to 37,800 between 2009 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 5400 to 37,800 between 2009 and 2015, we can solve for this constant of proportionality:
Example Question #111 : Constant Of Proportionality
The rate of growth of the number of pine martens in a section of Napa County is proportional to the population. The population increased by 38.9 percent 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 by 38.9 percent between 2012 and 2015, we can solve for this constant of proportionality:
Example Question #1001 : Rate
The rate of growth of the number of moths in the wardrobe leading to a land of talking animals is proportional to the population. The population increased by 17.5 percent between January and April. 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 by 17.5 percent between January and April, we can solve for this constant of proportionality. Mind the units that we're looking for, though it may be helpful to treat the months as their number in the calendar:
Example Question #2801 : Functions
The rate of growth of the number of E. coli cells in a forgotten slab of hamburger is proportional to the population. The population increased by 300 percent between 3:00 and 5:00. 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 by 300 percent between 3:00 and 5:00, we can solve for this constant of proportionality. Be mindful of the units requested:
Example Question #3836 : Calculus
The rate of growth of the number of electric eels in Baldwin's Lake is proportional to the population. The population increased by 19.6 percent 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 by 19.6 percent between 2012 and 2015, we can solve for this constant of proportionality:
Example Question #1011 : Rate
The rate of growth of the number of mongooses in Dale's Wild Woodland Safari is proportional to the population. The population increased by 59.2 percent between January of 2014 and February of 2015. 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 by 59.2 percent between January of 2014 and February of 2015, a timeframe of 13 months, we can solve for this constant of proportionality:
Example Question #3838 : Calculus
The rate of growth of the number of man-of-war jellyfish due to climate change is proportional to the population. The population increased by 125.4 percent 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 by 125.4 percent between 2013 and 2015, we can solve for this constant of proportionality:
Example Question #3839 : Calculus
The rate of change of the beluga population in an overhunted location is proportional to the population. The population decreased by 92.3 percent 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 decreased by 92.3 percent between 2013 and 2015, we can solve for this constant of proportionality:
Example Question #111 : How To Find Constant Of Proportionality Of Rate
The rate of change of the number of E. coli baceteria after exposure to a disinfectant is proportional to the population. The population decreased by 93.1 percent between 3:15 and 4:00. What is the constant of proportionality in hours-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 93.1 percent between 3:15 and 4:00, we can solve for this constant of proportionality. Given the units requested in the problem statement, convert the minutes to the decimals of an hour by dividing by 60:
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