Question

D(t)=256⋅(14)t9.7 Complete the following sentence about the decay rate of the temperature difference. The temperature difference is reduced by a factor of \dfrac 14 4 1 ​ start fraction, 1, divided by, 4, end fraction every seconds.

Answer 1

Using exponential function concepts, it is found that the correct sentence is given by:

The temperature difference is reduced by a factor of $\frac{3}{4}$ every 9.7 seconds.

What is an exponential function?

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^\frac{t}{n}$

In which:

• A(0) is the initial value.

• r is the decay rate every n instants of time, as a decimal.

In this problem, the function is given by:

$D(t) = 256\left(\frac{1}{4}\right)^{\frac{t}{9.7}}$

The decay rate is given by:

$1 - r = \frac{1}{4} \rightarrow r = \frac{3}{4}$

Hence, the sentence is:

The temperature difference is reduced by a factor of $\frac{3}{4}$ every 9.7 seconds.

More can be learned about exponential function concepts at brainly.com/question/25537936

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