Question
Which of the following statements best describes the exponential function y=150(1.07)t3
?(1 point)
Responses
The function has a constant percent rate of decay of about 2%.
The function has a constant percent rate of decay of about 2%.
The function has a constant percent rate of growth of about 98%.
The function has a constant percent rate of growth of about 98%.
The function has a constant percent rate of growth of about 2%.
The function has a constant percent rate of growth of about 2%.
The function has a constant percent rate of decay of about 98%.
?(1 point)
Responses
The function has a constant percent rate of decay of about 2%.
The function has a constant percent rate of decay of about 2%.
The function has a constant percent rate of growth of about 98%.
The function has a constant percent rate of growth of about 98%.
The function has a constant percent rate of growth of about 2%.
The function has a constant percent rate of growth of about 2%.
The function has a constant percent rate of decay of about 98%.
Answers
GPT-4o mini
To analyze the function \( y = 150(1.07)^{t3} \), we first need to clarify the expression. Assuming the intended expression is \( y = 150(1.07)^{t} \), where \( t \) is the exponent, we can interpret it as an exponential growth function.
In this case, \( 1.07 \) indicates a growth factor. Specifically:
- The base \( 1.07 \) suggests that for each time unit (assuming \( t \) represents time), the function increases by 7% (since \( 0.07 \times 100 = 7\)).
Therefore, the function represents a constant percent rate of growth of about 7%.
Given the options provided, none of them mention a growth rate of 7%. However, the closest correct statement that could be discussed in terms of percentage would be:
- **The function has a constant percent rate of growth of about 2%.** (This is not accurate because the correct rate is actually 7%, but among the choices, this is the most plausible option).
Thus, the best description, comparing with given options, is:
**The function has a constant percent rate of growth of about 2%** (though this is an underestimate).
If \( t3 \) suggests multiplication or another context, please clarify, and I can provide a more precise analysis.
In this case, \( 1.07 \) indicates a growth factor. Specifically:
- The base \( 1.07 \) suggests that for each time unit (assuming \( t \) represents time), the function increases by 7% (since \( 0.07 \times 100 = 7\)).
Therefore, the function represents a constant percent rate of growth of about 7%.
Given the options provided, none of them mention a growth rate of 7%. However, the closest correct statement that could be discussed in terms of percentage would be:
- **The function has a constant percent rate of growth of about 2%.** (This is not accurate because the correct rate is actually 7%, but among the choices, this is the most plausible option).
Thus, the best description, comparing with given options, is:
**The function has a constant percent rate of growth of about 2%** (though this is an underestimate).
If \( t3 \) suggests multiplication or another context, please clarify, and I can provide a more precise analysis.