The value of the tv is $1500. its value decreases by 14% each year. (a) write a function that represents the value y (in dollars) of the tv after t years. (b) find the approximate monthly percent decrease in value. round to the nearest tenth. (c) graph of the function from part (a). use the graph to estimate the value of tv after 3 years.

Part A)

Part B) The monthly percent decrease is about 1.3%

Part C) The value of TV after 3 years is about $950

Step-by-step explanation:

Part A) write a function that represents the value y (in dollars) of the TV after t years.

we know that

The exponential decay function is given by

where

y is the value in dollars of the TV

t is the number of years

a is the initial value

r is the rate of decay

In this problem we have

substitute

Part B) Find the approximate monthly percent decrease in value

we know that

I can rewrite the variable t as

Rewrite the function as

using Power of a Power Property

Find the decay rate

therefore

The monthly percent decrease is about 1.3%

Part C) Graph of the function from part (a). Use the graph to estimate the value of TV after 3 years

we have

using a graphing tool

see the attached figure

From the graph

For t=3 years

The value of y is approximate 950

therefore

The value of TV after 3 years is about $950

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation:

make sure you have version 2.50

try looking in the very back of the book : )

step-by-step explanation:

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