A flat-screen television costs $724.89 when it is new. The value of the television is expected to change by −12 3/5% per year. What is the expected value, to the nearest cent, of the television after 4 years?

Answers

Answer 1
653 no explanation needed it’s just 653
Answer 2

The solution is $ 422.98

The expected value of the television after 4 years is $ 422.98

What is exponential growth factor?

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the initial amount of the television be x₀

The value of x₀ = $ 724.89

Now , value of the television is expected to change by -12 3/5 % per year

So , the exponential decay rate of the television is r = -12 3/5 %

The rate r = -63/5 %

The rate r = -12.6 %

The number of years t = 4 years

So , the exponential decay rate of the television after 4 years is calculated from the formula

x ( t ) = x₀ × ( 1 + r )ⁿ

Substituting the values in the equation , we get

x ( 4 ) = 724.89 ( 1 - ( 12.6/100 ) )⁴

On simplifying the equation , we get

x ( 4 ) = 724.89 ( 1 - 0.126 )⁴

x ( 4 ) = 724.89 ( 0.874 )⁴

x ( 4 ) = 724.89 x 0.583506543376

x ( 4 ) = $ 422.978

So , rounding to the nearest cent , we get

The value of x ( 4 ) = $ 422.98

Hence , The expected value of the television after 4 years is $ 422.98

To learn more about exponential growth factor click :

https://brainly.com/question/13674608

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Answers

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