You purchase a cell phone for $$ \$ 125 $$. The value of the cell phone will decrease by about $$ 20 \% $$ each year. Write an equation to model the value of the phone as a function of time. Find the value of the phone after 3 years.

Question

UpStudy AI · Accepted Answer

To model the depreciation of the cell phone's value over time, you can use an exponential decay function. Here's how you can set it up and calculate the value after 3 years:

### 1. **Define the Variables**
- **Initial Value ($$ V_0 $$)**: \$125
- **Depreciation Rate**: 20% per year (which means the phone retains 80% of its value each year)
- **Time ($$ t $$)**: Number of years

### 2. **Write the Depreciation Equation**
The general formula for exponential decay is:

$$
V(t) = V_0 \times (1 - r)^t
$$

Where:
- $$ V(t) $$ is the value after $$ t $$ years.
- $$ V_0 $$ is the initial value.
- $$ r $$ is the depreciation rate.

Plugging in the given values:

$$
V(t) = 125 \times (0.8)^t
$$

### 3. **Calculate the Value After 3 Years**
Substitute $$ t = 3 $$ into the equation:

$$
V(3) = 125 \times (0.8)^3
$$

First, calculate $$ (0.8)^3 $$:

$$
0.8 \times 0.8 \times 0.8 = 0.512
$$

Now, multiply by the initial value:

$$
V(3) = 125 \times 0.512 = 64
$$

### **Final Answer**
- **Equation**: $$ V(t) = 125 \times (0.8)^t $$
- **Value After 3 Years**: \$64
The value of the phone after 3 years is \$64.

You purchase a cell phone for \( \$ 125 \). The value of the cell phone will decrease by about \( 20 \% \) each year. Write an equation to model the value of the phone as a function of time. Find the value of the phone after 3 years.

Solución de tutoría real

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions