Question
A population of deer is increasing exponentially. Which exponential equation in the form y=abx represents the situation shown in the graph? (1 point) Responses y=90(3)x y is equal to 90 times 3 to the x th power y=60(23)x y is equal to 60 times 2 thirds to the x th power y=90(52)x y is equal to 90 times 5 halves to the x th power y=60(32)x
Answers
Answered by
GPT-4o mini
To determine the correct exponential equation from the given options, we want to identify the equation that best represents exponential growth. The general form of an exponential function is \( y = ab^x \), where:
- \( a \) represents the initial value (the y-intercept when \( x = 0 \)),
- \( b \) represents the growth factor.
Here’s how we analyze the provided options:
1. **y = 90(3)^x:** This means the initial population is 90 and it triples (grows by a factor of 3) with each unit increase in \( x \).
2. **y = 60(2/3)^x:** This would indicate an initial population of 60, but with a decay factor of \( 2/3 \) (which would not represent growth).
3. **y = 90(5/2)^x:** This indicates an initial population of 90 and a growth factor of \( 5/2 \) (which implies a substantial growth, as \( 5/2 > 1 \)).
4. **y = 60(3^2)^x:** This represents an initial population of 60 and a growth factor of \( 9^x \) (which is quite substantial for growth).
To summarize, the equations that imply growth are:
- \( y = 90(3)^x \)
- \( y = 90(5/2)^x \)
- \( y = 60(3^2)^x \)
The equation you would choose depends on the context and the actual population values. However, typically, for exponential growth with the highest growth factor from the options you provided, **y = 90(5/2)^x** would be the strongest form implying consistent exponential growth.
But, without a specific graph provided, we can't definitively assert the correct equation if we cannot see initial values or growth factors represented on the graph.
If you need a specific choice for representing exponential growth without visual input, you would typically lean toward:
**y = 90(5/2)^x** (largest growth factor with consistent increase).
Make sure to compare against the given graph for accuracy!
- \( a \) represents the initial value (the y-intercept when \( x = 0 \)),
- \( b \) represents the growth factor.
Here’s how we analyze the provided options:
1. **y = 90(3)^x:** This means the initial population is 90 and it triples (grows by a factor of 3) with each unit increase in \( x \).
2. **y = 60(2/3)^x:** This would indicate an initial population of 60, but with a decay factor of \( 2/3 \) (which would not represent growth).
3. **y = 90(5/2)^x:** This indicates an initial population of 90 and a growth factor of \( 5/2 \) (which implies a substantial growth, as \( 5/2 > 1 \)).
4. **y = 60(3^2)^x:** This represents an initial population of 60 and a growth factor of \( 9^x \) (which is quite substantial for growth).
To summarize, the equations that imply growth are:
- \( y = 90(3)^x \)
- \( y = 90(5/2)^x \)
- \( y = 60(3^2)^x \)
The equation you would choose depends on the context and the actual population values. However, typically, for exponential growth with the highest growth factor from the options you provided, **y = 90(5/2)^x** would be the strongest form implying consistent exponential growth.
But, without a specific graph provided, we can't definitively assert the correct equation if we cannot see initial values or growth factors represented on the graph.
If you need a specific choice for representing exponential growth without visual input, you would typically lean toward:
**y = 90(5/2)^x** (largest growth factor with consistent increase).
Make sure to compare against the given graph for accuracy!
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