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[null,"Exponential Rate of Growth"]
[]
[null," This graphing utility lets you investigate "]
[null,null,"  the rate of growth of"]
[null,null," exponential functions"]
[null,null,"  based on the base b."]
[]
[]
[null,"The graphs of the three exponential functions:"]
[null,null,"y = 2x,   y = ex,  and  y = 3x"]
[null,"are shown from x = -1 to x = 2."]
[]
[]
[null,"       Select the point of tangency x0 =",{"$nulls":3},{"$f":"E16","v":1.0099999999999998}]
[]
[{"$nulls":3},67,{"$f":"a+D16*(b-a)/100","v":1.0099999999999998}]
[]
[null,null,"and compare the slopes of the"]
[null,null,"three tangent lines."]
[{"$nulls":9},"At the point of tangency x0 =",null,null,{"$f":"x0","v":1.0099999999999998}]
[]
["Click each item below for suggestions and investigations",{"$nulls":8},"   the slope of the tangent line to y = 2x is",{"$nulls":4},{"$f":"2^x0*LN(2)","v":{"v":1.3959368009420068,"d":"1.396"}}]
[null,"   Item 1",{"$nulls":7},"   the slope of the tangent line to y = ex is",{"$nulls":4},{"$f":"EXP(x0)","v":{"v":2.745601015016916,"d":"2.746"}}]
[null,"   Item 2",{"$nulls":7},"   the slope of the tangent line to y = 3x is",{"$nulls":4},{"$f":"3^x0*LN(3)","v":{"v":3.3322449605404993,"d":"3.332"}}]
[null,"   Item 3"]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["      Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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["a =",-1]
["b =",2]
[]
[{"$f":"x0","v":1.0099999999999998},{"$f":"2^x0","v":2.0139111001134373}]
[]
["b = 2"]
[{"$f":"a","v":-1},{"$f":"2^A7","v":0.5}]
[{"$f":"b","v":2},{"$f":"2^A8","v":4}]
[]
[{"$f":"x0","v":1.0099999999999998},{"$f":"2^x0","v":2.0139111001134373}]
[{"$f":"x0+0.1","v":1.1099999999999999},{"$f":"2^x0+2^x0*LN(2)*0.1","v":2.153504780207638}]
[]
[]
["b = e"]
[{"$f":"a","v":-1},{"$f":"2.718^A15","v":0.36791758646063283}]
[{"$f":"b","v":2},{"$f":"2.718^A16","v":7.387524}]
[]
[{"$f":"x0","v":1.0099999999999998},{"$f":"EXP(1)^x0","v":2.745601015016916}]
[{"$f":"x0+0.1","v":1.1099999999999999},{"$f":"EXP(x0)+EXP(x0)*0.1","v":3.0201611165186075}]
[]
[{"$f":"x0","v":1.0099999999999998},{"$f":"EXP(x0)","v":2.745601015016916}]
[]
["b = 3"]
[{"$f":"a","v":-1},{"$f":"3^A24","v":0.3333333333333333}]
[{"$f":"b","v":2},{"$f":"3^A25","v":9}]
[]
[{"$f":"x0","v":1.0099999999999998},{"$f":"3^x0","v":3.0331400758135603}]
[{"$f":"x0+0.1","v":1.1099999999999999},{"$f":"3^x0+3^x0*LN(3)*0.1","v":3.36636457186761}]
[]
[{"$f":"x0","v":1.0099999999999998},{"$f":"3^x0","v":3.0331400758135603}]

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