The length t (in years) of a home mortgage of $150,000 at 8% interest can be approximated by the model t = 12.542 In(x - 1000 X > 1000 where x represents the monthly payment (in dollars) (see figure). 30 25 20 Length of mortgage (in years) 15 10+ 5 - x 2000 4000 6000 8000 10,000 Monthly payment (in dollars) (a) Use the model to approximate the length of a $150,000 mortgage at 8% interest when the monthly payment is $1140.67 and when the monthly payment is $1294.62. (Round your answers to the nearest year.) $1140.67 monthly payment yr $1294.62 monthly payment yr (b) Approximate the total amount paid over the term of the mortgage with a monthly payment of $1140.67 and with a monthly payment of $1294.62. (Round your answers to the nearest cent.) $1140.67 monthly payment $ $1294.62 monthly payment $ (c) Approximate the total interest charge for a monthly payment of $1140.67 and for a monthly payment of $1294.62. (Round your answers to the nearest cent.) $1140.67 monthly payment $ $1294.62 monthly payment $ See Section 4.3 in the ebook to read more about this topic