Question

1. a cars value depreciates according to $v(t) = 28000(0.88)^t$ where $t$ is years after purchase. what will the car be worth after 6 years? round to the nearest dollar. $\underline{quadquadquadquadquadquadquad}$

Explanation:

Step1: Substitute t = 6 into the formula

We have the formula for the car's value \( V(t)=28000(0.88)^{t} \). We need to find the value when \( t = 6 \), so we substitute \( t=6 \) into the formula: \( V(6)=28000(0.88)^{6} \)

Step2: Calculate \( (0.88)^{6} \)

First, calculate \( 0.88^{6} \). Using a calculator, \( 0.88^{6}\approx0.4644040448 \)

Step3: Multiply by 28000

Then, multiply this result by 28000: \( V(6)=28000\times0.4644040448 \approx 12992.1132544\)

Step4: Round to the nearest dollar

Rounding \( 12992.1132544 \) to the nearest dollar gives us 12992.

Answer:

12992