Subjects algebra

Exponential Rewrite A20Ff9

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Restate the problem:** You want to understand step 3 where we rewrite the function $y = 300 \left(\frac{1}{2}\right)^{-\frac{x}{68}}$. 2. **Recall the exponent rule:** For any positive number $a$ and any real number $m$, $a^{-m} = \frac{1}{a^m}$. 3. **Apply the rule:** Here, $\left(\frac{1}{2}\right)^{-\frac{x}{68}} = \frac{1}{\left(\frac{1}{2}\right)^{\frac{x}{68}}} = 2^{\frac{x}{68}}$ because $\frac{1}{\left(\frac{1}{2}\right)^m} = 2^m$. 4. **Rewrite the function:** So, $$ y = 300 \left(\frac{1}{2}\right)^{-\frac{x}{68}} = 300 \times 2^{\frac{x}{68}} $$ 5. **Explanation:** This shows the function as exponential growth with base 2 raised to the power $\frac{x}{68}$. **Final answer:** Step 3 uses the negative exponent rule to rewrite the function as $y = 300 \times 2^{\frac{x}{68}}$ which is easier to interpret as growth.