Math Calculus and Vectors- Lee

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$8000 is deposited into a compound interest savings account, compounded monthly. The annual interest rate is 6%. The total amount after x manths, f(x) is a function of x, f(x) = 8000(1 + 22" where x is the number of months. AROC: On average, how much interest is generated per month during the first 10 years? A secant line is drawn between (0, f(0)) and (120, f{(120)). LAy N TH F200-F(0) _ 14555174-8000 _ AROC = = o T g 54.63 (dollars/month) In the first 10 years, on average, $54.63 of interest is generated each month. nop| (120: 145331171} 1 00004 (0. 8000) L e e e 500D IROC: According to the graph, how fast is the interest being generated at the moment it turns year 107 A tangent line is drawn at (120, f(120)). The y-intercept is estimated to be (0, 5850) IROC = 71207590 = 72 54 (dollars/month) At the moment it turns to year 10, the deposit is generating $72.54 of interest per month. [(120, 14555.174) | (1 5850) Since the interest is generated at an increasing rate in an exponential growth, the IROC at x = 120 (months) is greater than the AROC between x = 0 and x = 120 (month). Also, we can infer that the IROC at x = 0 (month) should be less than the AROC