For each function, determine if it is Linear, Quadratic, Exponential, or None of the above given the table with x and y values.

Steps to Solve

1. Identify the values from the table

The given values are:

2. Calculate the ratios of ( y ) values

We can check if the function is exponential by calculating the ratio of consecutive ( y ) values to see if they are constant:

• For ( x = 5 ) and ( x = 4 ): $$ \frac{250}{1250} = 0.2 $$

• For ( x = 6 ) and ( x = 5 ): $$ \frac{50}{250} = 0.2 $$

• For ( x = 7 ) and ( x = 6 ): $$ \frac{10}{50} = 0.2 $$

• For ( x = 8 ) and ( x = 7 ): $$ \frac{2}{10} = 0.2 $$

Since the ratios are constant, the relationship appears to be exponential.

3. Confirm the form of the exponential function

To confirm it's exponential, we can observe that ( y ) seems to decrease by a factor of 5 as ( x ) increases by 1. This gives us a pattern suggesting an exponential function which generally has the form:

$$ y = a \cdot b^x $$

Based on our calculations, it seems we have:

• ( a = 1250 )
• ( b = \frac{1}{5} )

This can be verified further, but preliminary checks confirm an exponential nature.