Question

Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. Which best describes this function? It is linear because the graph decreases over time. It is linear because there is both an independent and a dependent variable. It is nonlinear because linear functions are increasing functions. It is nonlinear because linear functions increase or decrease at the same rate.

Answer 1

Answer:

D

Step-by-step explanation:

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Answer 2

A linear function is a function that has a constant rate of change of the

output per unit change in the values of the input.

• The statement that best describes the the function is it is nonlinear because linear functions increase or decrease at the same rate.

Reasons:

The initial rate of change of temperature with time = Quick (rapidly) Later change of temperature with time = Slowly (less rapidly)

Given that the tea is initially hot and is expected to cool, we have;

• The initial drop in temperature over a unit of time = Δy₁

• The later drop in temperature over the same unit of time = Δy₂

Where;

• Δy₁ > Δy₂

From the above, we get;

• The shape of the graph formed will concave up and decreasing, similar to the graph of exponential decay.

Which gives that the graph will be nonlinear because the rate of change

over a given time period is not constant.

Therefore;

• The correct option is it is nonlinear because linear functions increase or decrease at the same rate.

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