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We are given the function \( f(x) = 4^x \), where \( f(x) \) represents the number of caps sold in month \( x \). The question asks us to determine the month when the store sells 64 caps.

We can set up the equation:

\[
f(x) = 64
\]

Substitute the expression for \( f(x) \):

\[
4^x = 64
\]

Now, rewrite 64 as a power of 4. Since \( 64 = 4^3 \), we can set up the equation:

\[
4^x = 4^3
\]

By comparing the exponents, we get:

\[
x = 3
\]

Thus, the store sells 64 caps in **Month 3**, which corresponds to option **D**.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. What happens to the number of caps sold in month 5?
2. How would the formula change if the store sold caps in multiples of 5 instead of 4?
3. If the store sold 1024 caps, in what month would that happen?
4. What is the general formula for determining when any number of caps is sold?
5. How could the function change if the growth factor were exponential instead of by powers of 4?

**Tip:** To solve equations involving powers, always try to express both sides with the same base. This allows you to compare exponents easily.

The number of caps a new online store sells increases by a factor of 4 each month. The function f(x) = 4^x represents the number of caps sold in month x. When does the store sell 64 caps?

Solve the exponential growth problem where a store's cap sales increase by a factor of 4 each month. Learn how to solve f(x) = 4^x to find when the store sells 64 caps. This problem covers exponential functions and exponent comparison, suitable for Grades 8-10 students.

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