Question

The function g(x) = 12,500(0.91)x represents the value of a piece of farm equipment after x years. Approximately when will its value be half its original value?
A.
8.1 years

B.
7.3 years

C.
4.6 years

D.
3.9 years

Answer 1

Answer:

B. 7.3 years

Step-by-step explanation:

The question is wrong. The correct function is :

$g(x)=12500(0.91)^{x}$

We have the function $g(x)$ that represents the value of a piece of farm equipment after $x$ years.

This means that when $x=0$ its original value is :

$g(0)=12500(0.91)^{0}=12500$

Now we want to calculate approximately when will its value be half its original value. Then, we write :

$\frac{12500}{2}=6250$

$6250$ is half of its original value. We need to find $x$ that satisfies the following equation :

$g(x)=6250=12500(0.91)^{x}$

Solving for $x$ :

$6250=12500(0.91)^{x}$ ⇒

$0.5=(0.91)^{x}$

Now we apply natural logarithm to each side of the equation :

$ln(0.5)=ln[(0.91)^{x}]$

Using logarithm properties :

$ln(0.5)=ln[(0.91)^{x}]$ ⇒

$ln(0.5)=x[ln(0.91)]$

$x=\frac{ln(0.5)}{ln(0.91)}$ ⇒

$x$ ≅ $7.3496$

The correct option is B. 7.3 years