An antique chair was purchased in the year 2013 for $500. At the time of purchase, an appraiser estimated that the value would increase by 10% per year. According to the appraiser's estimate about the value of the chairwhich statements are true?

Select ALL that apply

A. Alinear model provides the best of the estimated values.

B. The value will increase by 30% in the first 3 years.

C. After 2 yearsthe value will be $605.

D. The rate of change of the value will decrease over time

E.The value will increase by $50 in the first year

Answer:

C and E

.................

The true statements are (C) After [tex]2[/tex] years the value will be $[tex]605[/tex]  and (E) The value will increase by $[tex]50[/tex] in the first year.

Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

In the first year, the value[tex]=[/tex] $[tex]500+500\times \frac{10}{100}[/tex]

                                         [tex]=500\left ( 1+\frac{10}{100} \right ) \\ =\left ( 500\times 1.1 \right )[/tex]

                                         [tex]=[/tex]$[tex]550[/tex]

Change in price=$[tex]50[/tex]

After 2 years, the price is=$[tex]550+[/tex]$[tex]550 \times\frac{10}{100}[/tex]

                                         =$[tex]550\times(1+\frac{10}{100} )[/tex]

                                         =$[tex]550\times(1.1)[/tex]

                                         =$[tex]605[/tex]

After 3 years, the price=$[tex]605+605\times\frac{10}{100}[/tex]

                                      [tex]=605(1+\frac{10}{100} )[/tex]

                                      [tex]=(605\times1.1)[/tex]

                                      [tex]=[/tex]$[tex]665.5[/tex]

Rate of change[tex]=\frac{(665.5-500)}{500} \times100[/tex]%

                        [tex]=\frac{165.5}{5}[/tex]%

                        [tex]=33.1[/tex]%

                        [tex]\neq 30%[/tex]%

According to the problem, an exponential pt model provides the best fit.

Therefore, the true statements are an option C and E.

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