Question

type the correct answer in each box. round the values to the nearest dollar.
five years ago, bill paid $30,000 for his new car. he wants to sell his car and creates this graph of a linear function to model the value of his car
the manager of a used car dealership models the value of the car with the exponential function ( m(t) = 30,000(0.85)^t )
(graph: y-axis labeled cost (thousand dollars) from -10 to 90, x-axis labeled years from -1 to 11. a line starts at (0, 30) and goes to (11, 10))
according to bill’s calculation, the value of the car after five years is (\boxed{quad}). according to the manager’s calculations, the value is (\boxed{quad})

Explanation:

Step1: Find linear function

The linear model has initial value $V_0 = 30000$, and x-intercept at $t=12$. Slope is $m = \frac{0 - 30000}{12-0} = -2500$. Linear function: $V(t)=30000 -2500t$.

Step2: Calculate Bill's 5-year value

Substitute $t=5$: $V(5)=30000 -2500(5) = 30000 -12500 = 17500$

Step3: Calculate manager's 5-year value

Substitute $t=5$ into $M(t)=30000(0.85)^t$: $M(5)=30000(0.85)^5$.
$0.85^5 = 0.85*0.85*0.85*0.85*0.85 = 0.4437053125$.
$M(5)=30000*0.4437053125 = 13311.159375$

Step4: Round manager's value

Round $13311.159375$ to nearest dollar = 13311

Answer:

1. $\boldsymbol{17500}$
2. $\boldsymbol{13311}$