a.
Use a graphing utility to graph each function.
a.
Answer to Problem 58E
Explanation of Solution
Calculation:
The amount paid toward the interest is
The amount paid toward the reduction of the principal is
Where
The given functions can be simplified as,
And,
Now, graph the functions as shown below:
Hence, the graph is shown above.
b.
Find the approximate time.
b.
Answer to Problem 58E
Explanation of Solution
Calculation: The amount paid toward the interest is
The amount paid toward the reduction of the principal is
Where
Let us consider that the monthly payment is evenly divided between interest and principle then,
On dividing both sides by
Adding
Taking natural logarithm of both sides
Subtract
Dividing both sides by
Hence,
c.
Conclude for a repayment period of
c.
Answer to Problem 58E
As the year decreases , the monthly payment increases, the graph becomes much more linear.
Explanation of Solution
Calculation:
The amount paid toward the interest is
The amount paid toward the reduction of the principal is
Where
The amount and interest paid towards the principle can be written as,
Now, graph corresponding to the function is,
Let us consider that the monthly payment is evenly divided between interest and principle then,
On dividing both sides by
Adding
Taking natural logarithm of both sides
Subtract
Dividing both sides by
Hence, we conclude from both the graphs,we can see that as the year decreases , the monthly payment increases, the graph becomes much more linear.
Chapter 3 Solutions
EBK PRECALCULUS W/LIMITS
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