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]
