Question #f3694

Aug 28, 2017

The value of the car is never equal to zero for $x \in \mathbb{R}$.

Explanation:

The function for the value of the car is given as $v = 40 , 000 {\left(1 - 0.3\right)}^{x} = 40 , 000 {\left(0.7\right)}^{x}$

We need to find when the value is zero, so let's set $v$ equal to zero:

$R i g h t a r r o w v = 0$

$R i g h t a r r o w 40 , 000 {\left(0.7\right)}^{x} = 0$

Dividing both sides by $40 , 000$:

$R i g h t a r r o w {\left(0.7\right)}^{x} = 0$

At this point, we cannot go any further algebraically to try and solve for $x$.

There are no real solutions to the equation.

Therefore, the value of the car is never equal to zero for $x \in \mathbb{R}$.