Question 614077
A business estimates that the value V(t) of office equipment is decreasing according to the function V(t)=13200(4)^-0.14t, where t represents the number of years that have elapsed since the equipment was purchased, and V(t) is in dollars. After how many years will the value of the equipment be $3300?
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Given:
{{{V(t)=13200(4)^-0.14t}}}
set V(t) t0 3300 and solve for t
{{{3300=13200(4)^-0.14t}}}
{{{(3300/13200)=(4)^-0.14t}}}
{{{0.25 = (4)^-0.14t}}}
take log base 4 of both sides:
{{{log(4,0.24) = -0.14t}}}
{{{log(0.24)/log(4) = -0.14t}}}
{{{log(0.24)/(-0.14log(4)) = t}}}
{{{7.35319 = t}}}
answer: 7.35 years