1. **State the problem:** We are given the function $f(x) = 35 \cdot 2^x$ and asked to describe its behavior as $x$ increases. 2. **Recall the formula and properties:** The function is an exponential function of the form $f(x) = a \cdot b^x$ where $a=35$ and $b=2$. Since $b=2 > 1$, the function exhibits exponential growth. 3. **Evaluate key points:** - At $x=0$, $f(0) = 35 \cdot 2^0 = 35 \cdot 1 = 35$. - For negative $x$, $2^x$ is a fraction between 0 and 1, so $f(x)$ approaches 0 but never reaches it. - For positive $x$, $2^x$ grows rapidly, so $f(x)$ increases quickly. 4. **Interpret behavior:** The function starts near zero for large negative $x$, then grows slowly at first, and then more rapidly as $x$ increases. 5. **Conclusion:** The function grows more rapidly as $x$ increases, matching option C. **Final answer:** C. The function grows more rapidly as $x$ increases.