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A can of soda is placed inside a cooler. As the soda cools, its temperature [tex]\(T(x)\)[/tex] in degrees Celsius is given by the function:
[tex]\[ T(x) = -4 + 26 e^{-0.041 x} \][/tex]
where [tex]\(x\)[/tex] is the number of minutes since the can was placed in the cooler.

Find the temperature of the soda after 12 minutes and after 18 minutes. Round your answers to the nearest degree.

Temperature after 12 minutes: [tex]\(\square \, ^\circ C\)[/tex]

Temperature after 18 minutes: [tex]\(\square \, ^\circ C\)[/tex]

Sagot :

GinnyAnswer
To determine the temperature of the soda after 12 minutes and after 18 minutes, we will use the given temperature function:
[tex]\[ T(x) = -4 + 26 e^{-0.041 x} \][/tex]
where [tex]\( x \)[/tex] represents the number of minutes since the can was placed in the cooler.

### Step 1: Calculate the temperature after 12 minutes

1. Set [tex]\( x = 12 \)[/tex] in the function:
[tex]\[ T(12) = -4 + 26 e^{-0.041 \times 12} \][/tex]

2. Compute the expression inside the exponent:
[tex]\[ e^{-0.041 \times 12} \][/tex]

3. Multiply the result by 26 and then add -4 to this value.

4. Round the final answer to the nearest degree.

After performing these calculations, we obtain:
[tex]\[ T(12) = 12 \, ^\circ C \][/tex]

### Step 2: Calculate the temperature after 18 minutes

1. Set [tex]\( x = 18 \)[/tex] in the function:
[tex]\[ T(18) = -4 + 26 e^{-0.041 \times 18} \][/tex]

2. Compute the expression inside the exponent:
[tex]\[ e^{-0.041 \times 18} \][/tex]

3. Multiply the result by 26 and then add -4 to this value.

4. Round the final answer to the nearest degree.

After performing these calculations, we obtain:
[tex]\[ T(18) = 8 \, ^\circ C \][/tex]

### Final Answers:

- Temperature after 12 minutes: [tex]\( 12 \, ^\circ C \)[/tex]
- Temperature after 18 minutes: [tex]\( 8 \, ^\circ C \)[/tex]
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