Chapter 7.7, Problem 19P

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?

To determine

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 $y=1000{\left(1+\frac{5}{100}\right)}^x$

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.