Question

I was hoping someone could help me find the answers

Answer 1

A) We will determine the annual rate of change between 1991 and 2006 as follows:

We replace the values in the expression and solve for r, thatt is:

`15000=34000(1+r)^(15)\Rightarrow(15)/(34)=(1+r)^(15)`
`\Rightarrow\sqrt[15]{(15)/(34)}=1+r\Rightarrow\Rightarrow r=\sqrt[15]{(15)/(34)}-1`
`\Rightarrow r=-0.0530926\ldots\Rightarrow r\approx-0.0531`

So, the annual rate of change between 1991 and 2006 was of approximately -5%.

B) The correct answer in percentage form is -5.31%.

C) If we assume that te car value continues to drop by the same percentage, for the year 210 would have been:

`S\approx34000(1-0.0531)^(19)\Rightarrow S\approx12057.49614`

So, the value would end up being approximately $12057.5.