Algebra 2 - Word problem

Question

Gus buys a new car for $35,000. Each year, the car’s value depreciates 12% (this means it loses 12% of its value each year). Gus models the value of his car for any given year after purchase using the function V(x), where x is time in years.

Which observations correctly describe V(x)? There may be more than one correct answer. Select all that apply.

The value of the car decreases less rapidly as time continues. This means V(x) decreases less rapidly as x increases.

 

 

The car is initially worth $35,000, so V(x) has an x-intercept at (35,000,0).

 

Time increases as the car’s value changes, so V(x) is an increasing function.

 

The value of the car begins at $35,000 and then decreases, so the domain of V(x) is (−∞,35000].

 

The car loses value over time, so V(x) is a decreasing function.

 

The value for time cannot be negative, so the domain of V(x) is (0,∞).

 

The value of the car decreases more rapidly as time continues. This means V(x) increases more rapidly as x increases.

Answer 1

V(x) = 35K(1-.12)^x = 35,000(.88)^x

x intercept = (35,000, 0) true

V(x) is Not an increasing function. It's a decreasing function, as V gets smaller as x gets larger

domain is not (-infinity, 35000). domain is [0, infinity) the allowable values of x

time cannot be negative so (0, infinity) is almost right but domain also includes 0. domain is not an open interval at both ends

last statement is False