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# Natural Logarithmic Function

The term t (in years) of a \$120,000 home mortgage at 10% interest can be approximated by t = 5.315 / (-6.7968 + log(x)), x > 1000, where x is the monthly payment in dollars. [this problem is meant to be solved using a graphing utility]

a) Use a graphing utility to graph the model. [No problem; I have Maple]

b) Use the model to approximate the term of a home mortgage for which the monthly payment is \$1167.41. What is the total amount paid?

c) Use the model to approximate the term of a home mortgage for which the monthly payment is \$1068.45. What is the total amount paid?

d) Find the instantaneous rate of change of t with respect to x when x = 1167.41 and x = 1068.45.

e) Write a short paragraph describing the benefit of the higher monthly payment.

#### Solution Preview

a) I do not have a graphing utility. You have no problem to do it because you have Maple.
b) When the monthly payment is x = \$1167.41, we can use the model to calculate the term
t = 5.315 / (-6.7968 + log(1167.41)) = 20 years
...

#### Solution Summary

This solution is comprised of a detailed explanation to use a graphing utility to graph the model.

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