Question 179674
-Tessa has an antique plate valued at $75. It is expected to increase in value 8% per year.

a.) how would you write a function for the value of the plate in t years? 
{{{f(t) = 75*(1.08)^t}}}
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b.) how would you find out how much it would be worth in 10 years?
{{{f(t) = 75*(1.08)^10}}}
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Use a calc to find 1.08^10
f(t) = 75*2.158925
f(t) = $161.92 value after 10 yrs
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c.) how would you find out when the plate would reach a value of $200?
f(t) = {{{75*(1.08)^t}}}
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Substitute 200 for f(t)
{{{75*(1.08)^t}}} = 200
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Divide both sides by 75
{{{(1.08)^t}}} = {{{200/75}}}
{{{(1.08)^t}}} = {{{8/3}}}
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use the log equiv of exponent
{{{t*log(1.08)}}} = {{{log(8/3)}}}
find the log of both sides
.03342t = .42597
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t = {{{.42597/.03342}}}
t = 12.74 years to become valued at $200
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Check solution on a calc; enter: 75*(1.08)^12.74 = 199.93 ~ 200, close enough
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Any questions about this?