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 answer

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.