If the rate of inflation is 2%, the cost of an item in future years can be found by iterating the function #c(x)=1.02x#, how do you find the cost of a $70 portable stereo in four years if the rate of inflation remains constant?

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If the rate of inflation is 2%, the cost of an item in future years can be found by iterating the function #c(x)=1.02x#, how do you find the cost of a $70 portable stereo in four years if the rate of inflation remains constant?

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Answer 1 · 2017-07-14T06:27:39

#75.77#

Explanation:

Note that adding on #2%# can be shown as:

#100%+2% =102% = 102/100 = 1.02#

Multiplying a quantity by #1.02# is a way of increasing it by #2%# in one step.

If this increase happens to an amount #(x)# every year we have:
#year 1 " "rarr" "year 2" "rarr" "year 3" "rarr" "year 4#
#""x" "xx1.02 rarr" "xx1.02" "xx1.02" "xx 1.02#

Therefore after #4# years, the value can be calculated as:

#70 xx 1.02^4#

#= $75.77#

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If the rate of inflation is 2%, the cost of an item in future years can be found by iterating the function #c(x)=1.02x#, how do you find the cost of a $70 portable stereo in four years if the rate of inflation remains constant?

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