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Example Questions
Example Question #21 : How To Find Constant Of Proportionality Of Rate
The rate of growth of the number of fungal cells on a loaf of bread is proportional to the population. The population increased from 112 to 357 between 1:00 and 2:00. What is the expected population at 3:00?
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 is an initial population value, and
is the constant of proportionality.
Since the population increased from 112 to 357 between 1:00 and 2:00, we can solve for this constant of proportionality:
Using this, we can calculate the expected value from 2:00 to 3:00:
Example Question #3741 : Calculus
The rate of growth of the bacteria in a petri dish is proportional to the population. The population increased from 29 to 167 between 3:00 and 6:00. What is the expected population in 8:30?
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 is an initial population value, and
is the constant of proportionality.
Since the population increased from 29 to 167 between 3:00 and 6:00, we can solve for this constant of proportionality:
Using this, we can calculate the expected value from 6:00 to 8:30:
Example Question #921 : Rate
The rate of decrease due to poaching of the elephants in unprotected Sahara is proportional to the population. The population in one region decreased from 1038 to 817 between 2010 and 2015. What is the expected population in 2017?
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 is an initial population value, and
is the constant of proportionality.
Since the population decreased from 1038 to 817 between 2010 and 2015, we can solve for this constant of proportionality:
Using this, we can calculate the expected value from 2015 to 2017:
Example Question #27 : How To Find Constant Of Proportionality Of Rate
The rate of decrease in the population of grey wolves in Tennessee is proportional to the population. The population decreased from 5430 to 3740 between 2008 and 2015. What is the expected population in 2020?
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 is an initial population value, and
is the constant of proportionality.
Since the population decreased from 5430 to 3740 between 2008 and 2015, we can solve for this constant of proportionality:
Using this, we can calculate the expected value from :
Example Question #921 : Rate
The rate of growth of the population of prokaryotes in a pond is proportional to the population. The population increased from 1130 to 1460 between 3:15 and 4:30. What is the expected population in 6:45?
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 is an initial population value, and
is the constant of proportionality.
Since the population increased from 1130 to 1460 between 3:15 and 4:30, we can solve for this constant of proportionality. Convert the minutes to decimal values of an hour:
Using this, we can calculate the expected value from 4:30 to 6:45:
Example Question #22 : How To Find Constant Of Proportionality Of Rate
The rate of growth of the constituency of the hivemind is proportional to the population. The population increased from 10800 to 25200 between April and June. What is the expected population in November, when mankind takes its last stand?
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 is an initial population value, and
is the constant of proportionality.
Since the population increased from 10800 to 25200 between April and June, we can solve for this constant of proportionality. Use the months' number in the calendar:
Using this, we can calculate the expected value in November from June:
Good luck, humanity.
Example Question #31 : How To Find Constant Of Proportionality Of Rate
The rate of decrease of baceterial cells in response to a new antibiotic is proportional to the population. The population decreased from 15800 to 6540 between 3:15 and 4:00. What is the expected population at 8:30?
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 is an initial population value, and
is the constant of proportionality.
Since the population decreased from 15800 to 6540 between 3:15 and 4:00, we can solve for this constant of proportionality. Treat the minutes as decimal values for the hour:
Using this, we can calculate the expected value from 4:00 to 8:30:
Example Question #2721 : Functions
The rate of growth of the population of electric mice in Japan is proportional to the population. The population increased from 1800 to 2500 between 2012 and 2015. Determine the expected population in 2018.
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 is an initial population value,
represents a measure of elapsed time relative to this population value, and
is the constant of proportionality.
Since the population increased from 1800 to 2500 between 2012 and 2015, we can solve for this constant of proportionality:
Now that the constant of proportionality is known, we can use it to find an expected population value relative to an initial population value due to the difference in time points:
Example Question #3751 : Calculus
The rate of growth of the bacteria in a petri dish is proportional to the population. The population increased from 4900 to 7193 between 3:54 and 4:21. Determine the expected population at 5:12.
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 is an initial population value,
represents a measure of elapsed time relative to this population value, and
is the constant of proportionality.
Since the population increased from 4900 to 7193 between 3:54 and 4:21, we can solve for this constant of proportionality. Treat the minutes as decimals of an hour by dividing by 60:
Now that the constant of proportionality is known, we can use it to find an expected population value relative to an initial population value due to the difference in time points:
Example Question #3752 : Calculus
The rate of growth of the yeast in a loaf of bread is proportional to the population. The population increased from 178 to 413 between 3:15 and 3:45. Determine the expected population at 5:20.
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 is an initial population value,
represents a measure of elapsed time relative to this population value, and
is the constant of proportionality.
Since the population increased from 178 to 413 between 3:15 and 3:45, we can solve for this constant of proportionality. Treat the minutes as decimals after the hour by dividing them by 60:
Now that the constant of proportionality is known, we can use it to find an expected population value relative to an initial population value due to the difference in time points:
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