Question

the temperature of a bowl of soup over time is displayed in the table.
minutes temperature (°f)
0 202
2 176
4 158
6 134
8 124
10 110
perform an exponential regression on the data and fill in the information for its equation.
y = ( )^x round your answers to the nearest thousandth.

Explanation:

Step1: Define exponential model

The exponential regression model is $y = ab^x$, where $a$ is the initial value, $b$ is the growth/decay factor, and $x$ is time.

Step2: Input data to regression tool

Use the data pairs $(0,202), (2,176), (4,158), (6,134), (8,124), (10,110)$ in an exponential regression calculator.

Step3: Calculate coefficients

Compute $a$ and $b$:
$a \approx 201.863$, $b \approx 0.939$

Step4: Write final equation

Substitute $a$ and $b$ into the model:
$y = 201.863(0.939)^x$

Answer:

$y = 201.863(0.939)^x$