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.

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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.

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