try it! rich is comparing the cost of maintaining his car with the depreciating value of the car. when will…

Answer:

1. First, establish two functions:
   • The value function of the car $V(t)$: The initial value of the car is $V_0 = 20000$, and it decreases by 15% per - year. So the formula for the value of the car after $t$ years is $V(t)=20000\times(1 - 0.15)^t=20000\times0.85^t$.
   • The maintenance - cost function $M(t)$: The initial maintenance cost is $M_0 = 500$, and it increases by 28% per year. So the formula for the maintenance cost after $t$ years is $M(t)=500\times(1 + 0.28)^{t - 1}$ (for $t\geq1$).
2. To use a graphing calculator's table:
   • Enter the function $Y_1 = 20000\times0.85^X$ into the graphing calculator. Here, $X$ represents the number of years $t$.
   • Enter the function $Y_2 = 500\times1.28^{X - 1}$ into the graphing calculator.
   • Then, access the table function on the graphing calculator. Set an appropriate range for the values of $X$ (e.g., start from $X = 1$ and increment by 1).
   • Look for the value of $X$ (number of years) for which $Y_1$ (value of the car) and $Y_2$ (maintenance cost) are approximately equal.

Explanation:

Step1: Define value function

$V(t)=20000\times0.85^t$

Step2: Define maintenance - cost function

$M(t)=500\times1.28^{t - 1}$

Step3: Enter functions in calculator

Enter $Y_1 = 20000\times0.85^X$ and $Y_2 = 500\times1.28^{X - 1}$

Step4: Use table function

Set range for $X$ and look for equal $Y$ values.