Calculus 1 : How to find constant of proportionality of rate

Study concepts, example questions & explanations for Calculus 1

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Example Questions

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Example Question #191 : Constant Of Proportionality

Find the direct constant of proportionality of  from 

Possible Answers:

Correct answer:

Explanation:

To find direct constant of proportionality , you need to find the slope of the line between the two points at  and . To do so we use the formula:

Example Question #2 : Comparing Relative Magnitudes (Exponential Growth,Logarithmic Growth, Polynomial Growth)

The rate of growth of the population of Reindeer in Norway is proportional to the population. The population increased from 9876 to 10381 between 2013 and 2015. What is the expected population in 2030?

Possible Answers:

Correct answer:

Explanation:

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 9876 to 10381 between 2013 and 2015, we can solve for this constant of proportionality:

Using this, we can calculate the expected value from 2015 to 2030:

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