Tonya and Leo each bought a cell phone at the same time. The trade-in values, in dollars, of the cell phones are modeled by the given functions, where x is the number of months that each person has owned the phone. Tonya's Phone Leo's Phone f(x) =490(0.88)x x g(x) 0 480 2 360 4 270 phone has the greater initial trade-in value. During the first four months, the trade-in value of Tonya's phone decreases at an average rate the trade-in value of Leo's phone.

The answer is Tonya's phone had the greater initial trade-in value.

Leo's phone decreases at an average rate slower than the trade in value of Tonya's phone.

Step-by-step explanation:

Given

Tonya

Leo

Solving (a): The phone with greater initial value

The initial value is when x = 0. So, we have:

From Leo's table

By comparison;

i.e.

So: Tonya's had the greater initial trade-in value

Solving (b): The phone with lesser rate

An exponential function is:

Where:

For Tonya

For Leo, we have:

So, the equation becomes:

and

Solving , we have:

becomes

Divide both sides by 480

Take square roots

-- Leo's rate

By comparison; Leo's rate is slower i.e. 0.87 < 0.88