1. **State the problem:** We have the function $y = 50(2)^x$ representing the bacteria population $y$ after $x$ minutes. We need to determine if this is exponential growth or decay, find key features, and interpret them. 2. **Identify the type of function:** The general form of an exponential function is $y = a b^x$ where $a$ is the initial amount and $b$ is the base. 3. **Determine growth or decay:** If $b > 1$, the function represents exponential growth. If $0 < b < 1$, it represents exponential decay. 4. **Apply to our function:** Here, $a = 50$ and $b = 2$. Since $2 > 1$, this is exponential growth. 5. **Find the y-intercept:** The y-intercept occurs at $x=0$, so $$y = 50(2)^0 = 50 \times 1 = 50.$$ This means the initial bacteria count is 50. 6. **Domain:** Since time $x$ represents minutes after starting, it cannot be negative. So the domain is $x \geq 0$. 7. **Range:** Because the bacteria population grows exponentially and starts at 50, the range is $y \geq 50$. 8. **Interpretation:** As time increases, the bacteria population increases rapidly, doubling every minute. 9. **Summary:** - Exponential growth because base $2 > 1$. - Initial population 50 at $x=0$. - Domain $[0, \infty)$. - Range $[50, \infty)$. - Population doubles each minute. Final answer: The function represents exponential growth with initial bacteria count 50, domain $x \geq 0$, and range $y \geq 50$.