Evaluate the function for the given value.
$\begin{array}{c}
y=3 \cdot 3^x \text { for } x=1 \\
y=[?]\end{array}$
Answer (1)
Substitute x = 1 into the function y = 3 c d o t 3 x .
Calculate 3 1 = 3 .
Multiply the result by 3: y = 3 c d o t 3 = 9 .
The value of the function at x = 1 is 9 .
Explanation
Understanding the problem We are given the function y = 3 ⋅ 3 x and we need to evaluate it at x = 1 . This means we need to substitute x = 1 into the expression for y and simplify.
Substitution Substitute x = 1 into the function: y = 3 ⋅ 3 1
Simplification Now we simplify the expression. We know that 3 1 = 3 , so we have: y = 3 ⋅ 3 = 9
Final Answer Therefore, the value of the function y when x = 1 is 9.
Examples
Exponential functions are used to model population growth. For example, if a population of bacteria triples every hour, we can model the population size as a function of time using an exponential function similar to the one in this problem. Evaluating the function at a specific time tells us the population size at that time. Understanding exponential growth is crucial in fields like biology, finance, and computer science.
