document.write( "Question 127471: Two die- cast metal car models were purchased at the same time. The first cost $99.50 and appreciated by 10% yearly. The second cost $49.50 and appreciated 16% yearly. Algebraically determine how many years will it take for the two models to be of equal value. \n" ); document.write( "
Algebra.Com's Answer #93417 by ankor@dixie-net.com(22740)\"\" \"About 
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The first cost $99.50 and appreciated by 10% yearly. The second cost $49.50 and appreciated 16% yearly. Algebraically determine how many years will it take for the two models to be of equal value.
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\n" ); document.write( "Use the annual interest equation, t = time in years
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\n" ); document.write( "Cheap car value = expensive car value
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\n" ); document.write( "49.5(1.16)^t = 99.5(1.10)^t
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\n" ); document.write( "Using natural logs:
\n" ); document.write( "ln(49.5) + ln(1.16^t) = ln(99.50) + ln(1.10^t)
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\n" ); document.write( "log equiv of exponents:
\n" ); document.write( "ln(49.5) + t*ln(1.16) = ln(99.50) + t*ln(1.10)
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\n" ); document.write( "3.902 + .1484t = 4.6 + .0953t
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\n" ); document.write( ".1484t - .0953t = 4.6 - 3.902
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\n" ); document.write( ".0531t = .698
\n" ); document.write( "t = \".698%2F.0531\"
\n" ); document.write( "t = 13.14 years
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\n" ); document.write( "Find the value of each after 13.14 yrs, using a calc
\n" ); document.write( "1.16^13.14 * 49.5 = $348
\n" ); document.write( " 1.1^13.14 * 99.5 = $348 confirms our solution \n" ); document.write( "
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