1. The problem is to understand the function $k(x) = 5 \cdot 3^x$ for $x \geq 0$ and describe its behavior. 2. The function is an exponential function of the form $k(x) = a \cdot b^x$ where $a=5$ and $b=3$. 3. Important rules for exponential functions: - The starting value (when $x=0$) is $k(0) = a \cdot b^0 = a \cdot 1 = a$. - The base $b$ determines the growth factor. If $b>1$, the function grows exponentially. - For each increase of 1 in $x$, the output is multiplied by $b$. 4. Calculate the starting point: $$k(0) = 5 \cdot 3^0 = 5 \cdot 1 = 5$$ So the function starts at the point $(0,5)$. 5. Check the growth factor: For $x=1$, $$k(1) = 5 \cdot 3^1 = 5 \cdot 3 = 15$$ For $x=2$, $$k(2) = 5 \cdot 3^2 = 5 \cdot 9 = 45$$ Each time $x$ increases by 1, the output is multiplied by 3. 6. Therefore, the function starts at $(0,5)$ and the output increases by a factor of 3 for each integer increase in $x$. Final answer: The correct statement is "The function starts at $(0,5)$, then the output of the function increases by a factor of 3 for each integer increase of the input."