Evaluate the function for the given value.
[tex]
\begin{array}{c}
y=20 \cdot\left(\frac{1}{2}\right)^x \text { for } x=1 \\
y=[?]
\end{array}
[/tex]
Answer (2)
Substitute x = 1 into the function y = 20 c d o t ( 2 1 ) x .
Calculate y = 20 c d o t 2 1 .
Simplify the expression to find the value of y .
The final answer is 10 .
Explanation
Understanding the problem We are given the function y = 20 c d o t ( 2 1 ) x and we need to evaluate it at x = 1 . This means we need to substitute x = 1 into the function and calculate the value of y .
Substitution Substitute x = 1 into the function: y = 20 c d o t ( 2 1 ) 1
Calculation Now, we simplify the expression: y = 20 c d o t 2 1 = 10
Examples
Exponential decay functions like the one in this problem are used to model various real-world phenomena, such as the decay of radioactive substances, the cooling of an object, or the depreciation of an asset. For example, if you invest money in a savings account that loses half its value each year, this function can help you calculate how much money you'll have after a certain number of years. Understanding exponential decay is crucial in finance, physics, and other fields where quantities decrease over time.
By substituting x = 1 into the function and simplifying, we find that y = 10 . This demonstrates how exponential decay functions can be evaluated for specific values. The final answer is y = 10 .
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