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\frac{15}{34}=(1+r)^{15}$$\Rightarrow\sqrt[15]{\frac{15}{34}}=1+r\Rightarrow\Rightarrow r=\sqrt[15]{\frac{15}{34}}-1$$\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.