Question 1

Which of the following data plots may be modeled by an exponential function? &#8203;&#10;A) &#8203;  &#10;B) &#8203;  &#10;C) &#8203;  &#10;D) &#8203;

Accepted Answer

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Question 2

Evenly spaced data can be modeled by an exponential function if successive quotients are all the same.

Accepted Answer

If the successive quotients of the values in a dataset are all the same, it indicates a constant multiplicative rate of change, which is characteristic of an exponential function.

Question 3

If data are exponential, then only the first data point can be used to determine the initial value.

Accepted Answer

In an exponential function, the initial value can be determined from any data point, not just the first one, by using the formula of the exponential function and solving for the initial value.

Question 4

Data that decrease at an increasing rate are not exponential data.

Accepted Answer

Exponential data involve quantities that grow or decay at a rate proportional to their current value, which means they increase or decrease at a constant percentage rate, not at an increasing or decreasing rate. Data that decrease at an increasing rate suggest a different mathematical model, such as a quadratic or cubic function, rather than an exponential one.

Question 5

Data that show a constant percentage change can be modeled by an exponential function.

Accepted Answer

Exponential functions model situations where a quantity grows or decays at a constant percentage rate per unit of time, which is exactly what is described by data showing a constant percentage change.

Question 6

Which of the following data plots may be modeled by an exponential function? &#8203;&#10;A) &#8203;  &#10;B) &#8203;  &#10;C) &#8203;  &#10;D) &#8203;

Accepted Answer

The answer of Which of the following data plots may...

Question 7

If data are exponential, but the data are not measured in 1-unit increments, it is necessary to adjust the successive quotients in order to get the growth/decay factor.

Accepted Answer

When data are exponential but not measured in 1-unit increments, adjusting the successive quotients is necessary to accurately calculate the growth or decay factor, as the exponential rate is defined per unit increment.

Deck 18: Modeling Exponential Data