Question
Zena plant a bamboo stalk in her backyard. The height of the plant increased in height over the next few months. Which exponential equation in the form y=ab x represents the situation shown on the graph? (1 point) Responses y=4.5(3)x y is equal to 4 point 5 times 3 to the x th power y=3(32)x y is equal to 3 times 3 halves to the x th power y=3(23)x y is equal to 3 times 2 thirds to the x th power y=4.5(52)x
Answers
GPT-4o mini
To determine the correct exponential equation in the form \( y = ab^x \) that represents the growth of the bamboo stalk, we need to analyze the responses given.
1. **Examine the options:**
- **Option 1:** \( y = 4.5(3)^x \)
- **Option 2:** \( y = 3(32)^x \)
- **Option 3:** \( y = 3(23)^x \)
- **Option 4:** \( y = 4.5(52)^x \)
2. **Identifying growth patterns:**
- **Exponential Growth:** This typically involves a base greater than 1, which indicates growth.
- **Decay or Slow Growth:** A base of less than 1 indicates decay or slow growth.
3. **Logical Analysis:**
- **Option 1** \( y = 4.5(3)^x \) suggests rapid growth (exponential increase).
- **Option 2** \( y = 3(32)^x \) suggests extreme growth, not realistic for plant growth.
- **Option 3** \( y = 3(23)^x \) indicates a base greater than 1, suggesting rapid growth.
- **Option 4** \( y = 4.5(52)^x \) seems unrealistic for plant growth also.
Given that bamboos typically show exponential growth, the most reasonable choices here for a growing bamboo stalk would be between Option 1 and Option 3. Without more specific data points or a graph to analyze, **Option 1: \( y = 4.5(3)^x \)** is the most suitable answer as it suggests a realistic and continuous exponential growth rate.
Thus, the final answer is:
**\( y = 4.5(3)^x \)**
1. **Examine the options:**
- **Option 1:** \( y = 4.5(3)^x \)
- **Option 2:** \( y = 3(32)^x \)
- **Option 3:** \( y = 3(23)^x \)
- **Option 4:** \( y = 4.5(52)^x \)
2. **Identifying growth patterns:**
- **Exponential Growth:** This typically involves a base greater than 1, which indicates growth.
- **Decay or Slow Growth:** A base of less than 1 indicates decay or slow growth.
3. **Logical Analysis:**
- **Option 1** \( y = 4.5(3)^x \) suggests rapid growth (exponential increase).
- **Option 2** \( y = 3(32)^x \) suggests extreme growth, not realistic for plant growth.
- **Option 3** \( y = 3(23)^x \) indicates a base greater than 1, suggesting rapid growth.
- **Option 4** \( y = 4.5(52)^x \) seems unrealistic for plant growth also.
Given that bamboos typically show exponential growth, the most reasonable choices here for a growing bamboo stalk would be between Option 1 and Option 3. Without more specific data points or a graph to analyze, **Option 1: \( y = 4.5(3)^x \)** is the most suitable answer as it suggests a realistic and continuous exponential growth rate.
Thus, the final answer is:
**\( y = 4.5(3)^x \)**