Finding Equal Discounts in Pricing Models

A mobile phone store offers two pricing models for a particular smartphone. The first model offers a linear discount where the total price can be calculated using the equation:

$$ P(x) = 800 - 50x $$

where $$ P(x) $$ is the price in dollars after $$ x $$ discounts have been applied. The second model offers an exponential discount calculated using the formula:

$$ P(y) = 800 imes (0.8)^y $$

where $$ P(y) $$ is also the price in dollars after $$ y $$ discounts.

At what discount level do the prices offered by both models become equal? Select the value of $$ x $$ or $$ y $$ where this equality occurs.