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Math Calculus and Vectors- Lee

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1. create a non-linear function. Provide a real-world meaning of this function. 2. Use Desmos to graph one average rate of change and describe its meaning in this context. 3. Use Desmos to graph one instantaneous rate of change and describe its meaning in this context. $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