SOLUTION: A pizza restaurant purchases new equipment for $410,000 which depreciates in value at a rate of 9% annually. Write an equation for an exponential function f(t) that models the v

Algebra ->  Equations -> SOLUTION: A pizza restaurant purchases new equipment for $410,000 which depreciates in value at a rate of 9% annually. Write an equation for an exponential function f(t) that models the v      Log On


   



Question 1178238: A pizza restaurant purchases new equipment for $410,000 which depreciates in value at a rate of 9% annually.
Write an equation for an exponential function f(t) that models the value of the equipment over time.
f(t)=

Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

f(t)  =  410000%2A0.91%5Et,

where  t  is the time,  in years.

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To see many other similar  (and different)  solved problems,  look into the lesson
    - Problems on appreciated/depreciated values
in this site.




Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The depreciation of the value is an example of exponential decay.
When a quantity decreases by a fixed percent each year, or other period of
time, the amount f%28t%29 of that quantity after t years is given by:
f%28t%29=a%281-r%29%5Et
where a is the initial amount and r is the rate of decay
if given
R=9% ->r=0.09
a=410000
we have
f%28t%29=410000%281-0.09%29%5Et