Exponential growth graphing quiz with answer key

📚 Quick Study Guide

• 📈 Exponential Growth Definition: Exponential growth occurs when a quantity increases by the same factor over equal intervals of time.
• 🔢 General Formula: The general form of an exponential growth function is $y = a(1 + r)^x$, where:
  • $y$ is the final amount
  • $a$ is the initial amount
  • $r$ is the growth rate (as a decimal)
  • $x$ is the time interval
• 📝 Graphing Exponential Functions:
  • The graph starts near the x-axis and increases rapidly.
  • The base $(1 + r)$ is always greater than 1 for growth.
  • Identify key points such as the y-intercept ($a$).
• 💡 Key Characteristics: Exponential growth functions have a horizontal asymptote, typically at $y = 0$. They do not have a maximum value and increase without bound as $x$ increases.

🧪 Practice Quiz

1. What is the general form of an exponential growth function?
   1. $y = mx + b$
   2. $y = a(1 + r)^x$
   3. $y = ax^2 + bx + c$
   4. $y = a(1 - r)^x$
2. In the exponential growth function $y = a(1 + r)^x$, what does 'r' represent?
   1. The initial amount
   2. The time interval
   3. The growth rate
   4. The final amount
3. Which of the following statements is true about the graph of an exponential growth function?
   1. It decreases rapidly.
   2. It has a maximum value.
   3. It starts near the x-axis and increases rapidly.
   4. It has a vertical asymptote.
4. If a population of bacteria doubles every hour, which type of function best models its growth?
   1. Linear
   2. Quadratic
   3. Exponential
   4. Logarithmic
5. What is the y-intercept of the exponential growth function $y = 3(1.2)^x$?
   1. 0
   2. 1.2
   3. 3
   4. 3.6
6. An investment grows at a rate of 8% per year. Which value represents $(1 + r)$ in the exponential growth formula?
   1. 0.08
   2. 0.92
   3. 1.08
   4. 8
7. Which of the following equations represents exponential decay?
   1. $y = 5(1.5)^x$
   2. $y = 2(0.8)^x$
   3. $y = 3x + 2$
   4. $y = x^2 + 1$