Directions: answer the question by calculating the slope of the tangent line and the tangent- line equation, as appropriate.
Problem:Number of Banks
Base on data from 1984 to 2000 the number of different banks (not branches of banks) in the US may be modeled by:
B(t) = 2.970(t)^3 - 68.39(t)^2 - 170.9(t) + 18,172
banks, where t is the number of years since 1984.
How quickly was the # of banks decreasing in 2000? What was the estimated # of banks in 2001? (Use a tangent line approximation)
The solution is: 78.42 banks per yr. / 10,016 banks
My problem: I understand the whole tangent line concept - I am actually having the problem with getting the equation simplified before putting it into the tangent formula. (Everytime I try to multiply the B(16+h) to the t^3 it never works out nicely so that I can cancel out like terms)
Any help Would be appreciated VERY much!! I am desperate & frustrated since the easiest part of the problem is what I can't do!!
Thanks!!!
Problem:Number of Banks
Base on data from 1984 to 2000 the number of different banks (not branches of banks) in the US may be modeled by:
B(t) = 2.970(t)^3 - 68.39(t)^2 - 170.9(t) + 18,172
banks, where t is the number of years since 1984.
How quickly was the # of banks decreasing in 2000? What was the estimated # of banks in 2001? (Use a tangent line approximation)
The solution is: 78.42 banks per yr. / 10,016 banks
My problem: I understand the whole tangent line concept - I am actually having the problem with getting the equation simplified before putting it into the tangent formula. (Everytime I try to multiply the B(16+h) to the t^3 it never works out nicely so that I can cancel out like terms)
Any help Would be appreciated VERY much!! I am desperate & frustrated since the easiest part of the problem is what I can't do!!
Thanks!!!