First Part
We can see that the initial trade-in value of Leo's phone is 480. To find the trade-in value of Tonya's phone we would have to replace x=0 in the function. Doing so, we have:
[tex]f(0)=490(0.88)^0=490\cdot1=490\text{ (Using the rules of exponents)}[/tex]We can see that Tonya's phone has a greater initial trade-in value than Leo's phone.
Second Part
To find the average decreasing rate , we use the following formula:
[tex]\text{average decreasing rate=}\frac{\text{ (Trade-in vale after four months)-(Initial Trade-in value)}}{4\text{ (months)}}[/tex]We must find the trade-in value of Tonya's phone after four months. Doing so, we have:
[tex]\begin{gathered} f(4)=490(0.88)^4\text{ (Replacing x=4)} \\ f(4)=293.85\text{ (Raising 0.88 to the power 4 and multiplying)} \end{gathered}[/tex]Finding the average rate for Leo's phone, we have:
[tex]\text{ average of Leo's phone=}\frac{270-480}{4}=\frac{-210}{4}=-52.5[/tex]Finding the average rate for Tonya's phone, we have:
[tex]\text{average of Tonya's phone=}\frac{293.85-490}{4}=\frac{-196.15}{4}=-49.04[/tex]We can see that the trade-in value of Tonya's phone decreases at an average rate slower than the trade-in value of Leo's phone.