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17 March, 16:11

The formula m = 12,000 + 12,000 (0.05) t 12t gives Keri's monthly loan payment when the annual interest rate is 5% and t is the length of the loan, in years. What are the asymptotes of the function? Explain what the asymptotes represent in context.

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  1. 17 March, 16:31
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    This is for the question: The formula m = 12,000 + 12,000rt / 12t gives Keri's monthly loan payment, where r is the annual interest rate and t is the length of the loan, in years.

    Explain why the formula is a rational function for a given value of r. What if you are given t?

    It is of the form p (x) / q (x) where p (x) and q (x) are polynomials, and q (x) does not equal zero.

    If r is given, it does not change the fact that there is still a variable in the denominator.

    If t is given, there is no longer a variable in the denominator. The function is still rational, but the case of t being a constant, it is also linear.
  2. 17 March, 18:12
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    The vertical asymptote is x 0.

    The horizontal asymptote is y 50.

    The vertical asymptote shows there is no monthly payment for a loan of 0 years.

    The horizontal asymptote shows that as the length of time for which the loan is taken out increases, the monthly payment decreases. The monthly payment approaches, but never gets to $50 a month. This is because longer loans have greater simple interest up front.
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