Given t(x)=−6(12)x�(�)=−6(12)�, what is the value of t(−2)�(−2)?


To find the value of \( t(-2) \) given the function \( t(x) = -6 \times \left(\frac{1}{2}\right)^x \), follow these steps:

1. **Substitute** \( x = -2 \) into the function:
   \[
   t(-2) = -6 \times \left(\frac{1}{2}\right)^{-2}
   \]

2. **Simplify** the expression \( \left(\frac{1}{2}\right)^{-2} \):
   \[
   \left(\frac{1}{2}\right)^{-2} = \left(\frac{2}{1}\right)^2 = 2^2 = 4
   \]

3. **Multiply** the result by \(-6\):
   \[
   t(-2) = -6 \times 4 = -24
   \]

So, the value of \( t(-2) \) is \(\boxed{-24}\).

Do you have any questions or would you like more details? Here are five related questions you might find interesting:

1. What is the general form of an exponential function?
2. How does the sign of the exponent affect the result of an exponential expression?
3. Can exponential functions have negative bases?
4. How do you solve exponential equations algebraically?
5. What are the properties of the graph of an exponential function?

**Tip:** When dealing with negative exponents, remember that they represent the reciprocal of the base raised to the positive exponent.

Find the value of t(-2) in the exponential function t(x) = -6 * (1/2)^x. Step-by-step solution provided, covering negative exponents and exponential function properties. Suitable for Grades 9-12.

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