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Example Questions
Example Question #1 : Constant Of Proportionality
Suppose a blood cell increases proportionally to the present amount. If there were blood cells to begin with, and blood cells are present after hours, what is the growth constant?
The population size after some time is given by:
where is the initial population.
At the start, there were 30 blood cells.
Substitute this value into the given formula.
After 2 hours, 45 blood cells were present. Write this in mathematical form.
Substitute this into , and solve for .
Example Question #1 : Constant Of Proportionality
Given any linear function , determine the direct constant of proportionality
Direct constant of proportionality for any given function y, between any x values, is given by
, where is the direction constant of proportionality
In the case of a linear function
is the same thing as the slope.
Therefore, the constant of proportionality is
Example Question #1 : Constant Of Proportionality
Find the direct constant of proportionality of from to .
To determine the direct constant of proportionality, we determine the rate of change from and for .
Rate of change is determined by
.
In our case, between and , the rate of change is
.
Example Question #1 : How To Find Constant Of Proportionality Of Rate
Find the direct constant of proportionality of from to .
Direct constant of proportionality is given by
.
Since and
Example Question #21 : Exponential Functions
Suppose a population of bacteria increases from to in . What is the constant of growth?
None of these
The equation for population growth is given by . is the population, is the intial value, is time, and is the growth constant. We can plug in the values we know at time and solve for .
Now that we solved for , we can plug in what we know for time and solve for .
Example Question #1 : How To Find Constant Of Proportionality Of Rate
A population of deer grew from 50 to 200 in 7 years. What is the growth constant for this population?
None of these
The equation for population growth is given by . P is the population, is the intial value, is time, and is the growth constant. We can plug in the values we know at time and solve for .
Now that we have solved for we can solve for at
Example Question #4 : How To Find Constant Of Proportionality Of Rate
A population of mice has 200 mice. After 6 weeks, there are 1600 mice in the population. What is the constant of growth?
The equation for population growth is given by . is the population, is the intial value, is time, and is the growth constant. We can plug in the values we know at time and solve for .
Now that we have we can solve for at .
Example Question #4 : Constant Of Proportionality
Find the direct constant of proportionality of from to .
is undefined
Direct constant of proportionality is given by
, where is the change in the position and is the change in the position.
Since , and we're going from to
Example Question #1 : Exponential Growth Applications
The rate of decrease of the dwindling wolf population of Zion National Park is proportional to the population. The population decreased by 7 percent between 2009 and 2011. What is the constant of proportionality?
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 by 7 percent between 2009 and 2011, we can solve for this constant of proportionality:
Example Question #2 : How To Find Constant Of Proportionality Of Rate
The rate of growth of the Martian Transgalactic Constituency is proportional to the population. The population increased by 23 percent between 2530 and 2534 AD. What is the constant of proportionality?
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 by 23 percent between 2530 and 2534 AD, we can solve for this constant of proportionality:
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