Question: 1 — Introduction to Exponential Equations
LEARNING OBJECTIVE: Evaluate an exponential function for a given value of
x.
For the exponential function $f(x) = 4 \cdot 3^x$, what is the value of $f(2)$?
a.) 36
b.) 48
c.) 144
d.) 24
1. **State the problem:** We need to find the value of the exponential function $f(x) = 4 \cdot 3^x$ when $x = 2$.
2. **Recall the formula:** The function is given by $$f(x) = 4 \cdot 3^x$$ which means multiply 4 by 3 raised to the power of $x$.
3. **Substitute $x=2$ into the function:** $$f(2) = 4 \cdot 3^2$$
4. **Calculate the exponent:** $$3^2 = 3 \times 3 = 9$$
5. **Multiply:** $$f(2) = 4 \cdot 9 = 36$$
6. **Conclusion:** The value of $f(2)$ is $36$.
Therefore, the correct answer is **a.) 36**.