18,020=120(1-(1+0.4233)^-n/0.4233)I need to figure out what the value -n isAll the calculators i've used say it's not a real number, but I need it to be for a project. Can I also get a step by step?PLEASE HELP IT'S DUE TOMORROWI'll give a brainliest

Accepted Solution

Start with [tex]18020=120\left(1-\dfrac{(1+0.4233)^{-n}}{0.4233}\right)[/tex] Divide both sides by 120: [tex]\dfrac{18020}{120}=1-\dfrac{(1+0.4233)^{-n}}{0.4233}[/tex] Simplify the dfraction on the left hand side, and the sum in the parenthesis of the right hand side: [tex]\dfrac{901}{6}=1-\dfrac{(1.4233)^{-n}}{0.4233}[/tex] Subtract 1 from both sides: [tex]\dfrac{901}{6}-1=-\dfrac{(1.4233)^{-n}}{0.4233}[/tex] Change side to both sides: [tex]1-\dfrac{901}{6}=\dfrac{(1.4233)^{-n}}{0.4233}[/tex] Simplify the left hand side: [tex]-\dfrac{895}{6}=\dfrac{(1.4233)^{-n}}{0.4233}[/tex] Multiply both sides by 0.4233: [tex]-0.4233\cdot\dfrac{895}{6}=(1.4233)^{-n}[/tex] Simplify the left hand side: [tex]-\dfrac{378.8535}{6}=(1.4233)^{-n}[/tex] Apply the definition of negative exponents: [tex]-\dfrac{378.8535}{6}=\dfrac{1}{1.4233^n}[/tex] Invert both sides: [tex]-\dfrac{6}{378.8535}=1.4233^n[/tex] This is why the equation is impossible: the function [tex]f(x) = 1.4233^x[/tex] is an exponential function, and as such, it is always positive. So, there cannot be a value for [tex]n[/tex] such that the last equation is satisfied.