https://file.aiquickdraw.com/mathbot/file/1727977091834v7vfbsmz.jpg

How do I put this into a calculator. Does it turn into ln or something 

The expression you've uploaded is:

\[
\left( 1 - e^{-\frac{8 \, \text{s}}{(100,000 \, \Omega)(20 \times 10^{-6} \, \text{F})}} \right)
\]

This is an exponential decay formula, commonly seen in RC (resistor-capacitor) circuits, where:

- \( R = 100,000 \, \Omega \) (resistance)
- \( C = 20 \times 10^{-6} \, \text{F} \) (capacitance)
- \( t = 8 \, \text{s} \) (time)

The expression does **not** involve taking the natural logarithm directly (`ln`). However, the exponential term uses `e`, which is the base of the natural logarithm.

### Step-by-Step Instructions to Enter Into a Calculator:

1. **Calculate the time constant \( \tau \):**
   \[
   \tau = R \times C = 100,000 \, \Omega \times 20 \times 10^{-6} \, \text{F} = 2 \, \text{s}
   \]
2. **Find the ratio \( \frac{t}{\tau} \):**
   \[
   \frac{t}{\tau} = \frac{8 \, \text{s}}{2 \, \text{s}} = 4
   \]
3. **Substitute into the exponent:**
   \[
   1 - e^{-4}
   \]

4. **Calculate the exponential term \( e^{-4} \):**  
   On most calculators, you can input `e^(-4)` using an `e^x` button or similar.

   \( e^{-4} \approx 0.0183 \)

5. **Subtract from 1:**
   \[
   1 - 0.0183 = 0.9817
   \]

So, the final result of the expression is approximately **0.9817**.

Would you like more details or have any specific questions?

---

### Further Questions:
1. What does the time constant \( \tau \) represent in RC circuits?
2. How does the value of \( t \) (time) affect the result of the expression?
3. Why does this formula use the exponential function \( e \)?
4. How is the charging and discharging process of a capacitor modeled by this equation?
5. What is the significance of the factor \( 1 - e^{-t/\tau} \) in the formula?

### Tip:
For such calculations, it's handy to use scientific calculators or online tools that directly allow exponential functions like `e^x`.

How do I put this into a calculator. Does it turn into ln or something?

Learn how to evaluate the exponential decay formula for an RC circuit: 1 - e^(-t/RC). This guide covers the process of calculating time constant τ, exponent e^(-t/τ), and entering the result into a scientific calculator. Suitable for high school students (Grades 11-12).

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