An antique table increases in value according to the function ​v(x)equals750​(1.06​) Superscript x​ dollars, where x is the number of years after 1980.

Question

The value of the table was ​$
  
enter your response here in 2005.

Answer 1

To find the value of the antique table in 2005, we first need to determine how many years after 1980 it is.

2005 - 1980 = 25 years

Now we can use the value function given:

\[ v(x) = 750(1.06)^x \]

In this case, \( x = 25 \):

\[ v(25) = 750(1.06)^{25} \]

Now, let's calculate \( (1.06)^{25} \):

\[ (1.06)^{25} \approx 4.29187 \] (You can calculate this using a calculator.)

Now we can find the value of the table:

\[ v(25) = 750 \times 4.29187 \approx 3219.90 \]

So, the value of the table in 2005 was approximately $3219.90.