The value of Huda's business computer is decreasing by $$ 15 \% $$ each year. Its value, in dollars, $$ x $$ years from now will be $$ 3,000\left(\frac{17}{20}\right)^{x} $$. How much is the computer worth now? Show your work.

Question

UpStudy AI · Accepted Answer

To find the current value of Huda's business computer, we need to analyze the given information. The value of the computer decreases by $$ 15\% $$ each year, which means it retains $$ 85\% $$ of its value each year.

The formula for the value of the computer $$ V $$ after $$ x $$ years can be expressed as:

$$
V = V_0 \cdot (0.85)^x
$$

where $$ V_0 $$ is the current value of the computer.

According to the problem, the value of the computer $$ x $$ years from now is also given by:

$$
V = 3000 \left(\frac{17}{20}\right)^{x}
$$

Now, we can set these two expressions for $$ V $$ equal to each other:

$$
V_0 \cdot (0.85)^x = 3000 \left(\frac{17}{20}\right)^{x}
$$

To find $$ V_0 $$, we can rearrange the equation:

$$
V_0 = \frac{3000 \left(\frac{17}{20}\right)^{x}}{(0.85)^{x}}
$$

Now, we can simplify the right side. Notice that $$ \frac{17}{20} $$ can be expressed in terms of $$ 0.85 $$:

$$
\frac{17}{20} = 0.85
$$

Thus, we can rewrite the equation as:

$$
V_0 = 3000 \cdot \left(\frac{17}{20} \cdot \frac{1}{0.85}\right)^{x}
$$

Now, we can calculate $$ \frac{17}{20} \cdot \frac{1}{0.85} $$:

$$
\frac{17}{20} \cdot \frac{1}{0.85} = \frac{17}{20} \cdot \frac{20}{17} = 1
$$

This means that the expression simplifies to:

$$
V_0 = 3000
$$

Thus, the current value of Huda's business computer is:

$$
\boxed{3000}
$$
The current value of Huda's business computer is \$3,000.

The value of Huda’s business computer is decreasing by each year. Its value,
in dollars, years from now will be . How much is the computer worth
now? Show your work.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions

The value of Huda’s business computer is decreasing by each year. Its value, in dollars, years from now will be . How much is the computer worth now? Show your work.