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The internal temperature, in degrees Celsius, of an electric, convection oven was measured over a two-minute interval. The data Is shown below, where
t is measured in minutes.

t
0
0.5
1
1.5
2

^(@)C
18
29.677
48.929
80.670
133.003

Which of the following models best represents this situation as a function of time?
Elimination Tool
Setect one answer
A
C(t)=56.2 x+5.856
B
C(t)=18e^(t)
C
C(t)=18^(t)+17

The internal temperature, in degrees Celsius, of an electric, convection oven was measured over a two-minute interval. The data Is shown below, where $t$ is measured in minutes. $\newline$ \begin{tabular}{|c|c|c|c|c|c|c|} $\newline$ \hline $t$ & $0$ & $0$ . $5$ & $1$ & $1$ . $5$ & $2$ \\ $\newline$ \hline ${ }^{\circ} \mathrm{C}$ & $18$ & $29$ . $677$ & $48$ . $929$ & $80$ . $670$ & $133$ . $003$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ Which of the following models best represents this situation as a function of time? $\newline$ Elimination Tool $\newline$ Setect one answer $\newline$ A $C(t)=56.2 x+5.856$ $\newline$ B $C(t)=18 e^{t}$ $\newline$ C $C(t)=18^{t}+17$

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Evaluate two-variable equations: word problems

Full solution

Q. The internal temperature, in degrees Celsius, of an electric, convection oven was measured over a two-minute interval. The data Is shown below, where

t

is measured in minutes.

\newline

\begin{tabular}{|c|c|c|c|c|c|c|}

\newline

\hline

t

&

0

&

0

.

5

&

1

&

1

.

5

&

2

\\

\newline

\hline

{ }^{\circ} \mathrm{C}

&

18

&

29

.

677

&

48

.

929

&

80

.

670

&

133

.

003

\\

\newline

\hline

\newline

\end{tabular}

\newline

Which of the following models best represents this situation as a function of time?

\newline

Elimination Tool

\newline

Setect one answer

\newline

A

C(t)=56.2 x+5.856

\newline

B

C(t)=18 e^{t}

\newline

C

C(t)=18^{t}+17

Analyze Data and Models: Analyze the given data points and the models to determine which best fits the data. We have the temperature data at different times: $t = 0$ , $C = 18$ $t = 0.5$ , $C = 29.677$ $t = 1$ , $C = 48.929$ $t = 1.5$ , $C = 80.670$ $t = 2$ , $C = 133.003$ We need to check which model fits these data points best.
Test Initial Data Point: Test each model with the initial data point $t=0$ .
Model A: $C(t)=56.2 \times t + 5.856$
$C(0) = 56.2 \times 0 + 5.856 = 5.856$ (Does not match $C=18$ )
Model B: $C(t)=18e^{t}$
$C(0) = 18e^{0} = 18$ (Matches $C=18$ )
Model C: $C(t)=18^{t} + 17$
$C(0) = 18^{0} + 17 = 18 + 17 = 35$ (Does not match $C=18$ )
Only Model B matches the initial condition.
Confirm Model B: Test Model B with another data point for confirmation. $\newline$ Using $t=1$ , $C=48.929$ $\newline$ $C(1) = 18e^{1} \approx 18 \times 2.718 = 48.924$ (Close to $C=48.929$ ) $\newline$ This confirms that Model B continues to fit the data well.

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