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Writing Explain the difference in how you would model the following situations. Person A puts $1000 in a safe in his home, and puts in an additional $50 per year. Person B puts $1000 in an investment that earns 5% per year. Why is one exponential and the other linear? How would their graphs compare? How would their values compare over time?
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To explain: How would their values compare over time?
Explanation of Solution
Given information: Persons A puts $1000 in a safe in his home, and puts in an additional $50 per year. Person B puts $1000 in an investment that earns 5% per year
Calculation: For person A, every year there is fix increase of $50, every year increasing rate is same so its model is Linear.
Model for person A is of form y=1000+50x
For person B, every year there is increase in the amount that is earned so here we can use compound interest which is nothing but exponential function, so its model is exponential.
Model for person B is of form y=1000(1+5100)x
Graphs of both the Models is
Conclusion: After a long time the difference between the amount of A and B will increase rapidly. B's money will be much greater than A's money.
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High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
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