Constant Percent Rates of Change Quick Check

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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 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%.
The function has a constant percent rate of decay 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 98%.

The function has a constant percent rate of decay of about 2%.

1 answer

The exponential function given is \( y = 150(1.07)^{t3} \).

The key part to note here is the base of the exponent, which is \( 1.07 \).

  • A base greater than 1 indicates growth.
  • In this case, the growth rate can be found by taking the base minus 1: \( 1.07 - 1 = 0.07 \) or 7%.

Therefore, the correct statement would be:

The function has a constant percent rate of growth of about 7%.

However, since that option is not included in your provided responses, the closest related statement regarding the function that we have can be summarized as:

  • It does not have decay, thus eliminating those options.
  • The option that might seem closest is that the function has a constant percent rate of growth of about 2%, but this is misleading.

Make sure to check over the options provided as it seems they do not accurately reflect the correct growth rate from the function you provided.