Question

An antique table increases in value according to the function v(x)=550(1.05)x dollars, where x is the number of years after 1990.a. How much was the table worth in 1990?b. If the pattern indicated by the function remains valid, what was the value of the table in 2005?c. Use a table or a graph to estimate the year when this table will reach double its 1990 value

Answer 1

In 1990 the value of the antique table was:

`\begin{gathered} v(0)=550(1.05)^0, \\ v(0)=550\cdot1, \\ v(0)=550. \end{gathered}`

In 2005, x=2005-1990=15, therefore:

`\begin{gathered} v(15)=550(1.05)^(15)\text{.} \\ v(15)\approx1143.41. \end{gathered}`

Graphing the function we get:

Therefore, after approximately 14 years, the antique table will double its value, which corresponds to the year 2004.

Answer:

a) The table was worth $550 in 1990.

b) The value of the table was $1143.41 in 2005.

c) The antique table will double its value in 2004.