Transcendental function as power series?

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1 Answer
MattyMatty
May 17, 2018

#"a) 856.022 $"#
#"b) 15.4 years"#

Explanation:

#"a) "exp(x) = e^x = 1 + x + x^2/2 + x^3/6 + ...#
#t = 12, r = 0.045, P = 500#
#=> A = 500*e^(0.045*12) = 500*e^0.54#
#~~ 500*(1 + 0.54 + 0.54^2/2 + 0.54^3/6)#
#= 500*(1 + 0.54 + 0.1458 + 0.026244)#
#= 500*1.712044#
#= 856.022#

#"b) "A = 2P#
#=> 2P = P*e^(0.045*t)#
#=> 2 = e^(0.045*t)#
#=> ln(2) = 0.045*t#
#=> t = ln(2)/0.045 = 15.4" years"#

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