Question

select the correct answer from each drop - down menu.
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 p has owned the phone.

phone has the greater initial trade - in value.
during the first four months, the trade - in value of tonyas phone decreases at an average rate the trade - in value of leos p

Explanation:

Step1: Find the initial trade - in value

For Tonya's phone, when \(x = 0\), \(f(0)=490(0.88)^{0}\).
Since \(a^{0}=1\) for \(a
eq0\), \(f(0) = 490\).
For Leo's phone, when \(x = 0\), \(g(0)=480\).
Since \(490>480\), Tonya's phone has the greater initial trade - in value.

Step2: Calculate the average rate of change

The average rate of change formula is \(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\).
For Tonya's phone, \(x_1 = 0\), \(y_1=f(0)=490\), \(x_2 = 4\), \(y_2=f(4)=490(0.88)^{4}\).
\(f(4)=490\times0.59969536\approx293.85\).
The average rate of change \(m_{T}=\frac{293.85 - 490}{4-0}=\frac{-196.15}{4}=-49.0375\).
For Leo's phone, \(x_1 = 0\), \(y_1 = g(0)=480\), \(x_2 = 4\), \(y_2 = g(4)=270\).
The average rate of change \(m_{L}=\frac{270 - 480}{4-0}=\frac{-210}{4}=-52.5\).
Since \(\vert-49.0375\vert<\vert-52.5\vert\), the trade - in value of Tonya's phone decreases at an average rate slower than the trade - in value of Leo's phone.

Answer:

Tonya's; slower than