Quick help! Exponential modellingThe temperature (T) of a dish t minutes after it is removed from the microwave, is given by:[tex]T(t) = 55 \times ({0.913})^{t} +22°C[/tex]a) What is the initial temperature of the dish?b) What is the temperature after,(i) 12 minutes(ii) 36 minutes
Accepted Solution
A:
Answer:a) 77 degrees Celsius bi) 40.45066 degrees Celsiusbii) 24.0764 degree Celsius Step-by-step explanation:I'm assuming the temperature function is:[tex]T(t)=55(0.913)^t+22[/tex].a) The initial temperature can be found by replacing t with 0.[tex]T(0)=55(0.913)^0+22[/tex][tex]T(0)=55(1)+22[/tex][tex]T(0)=55+22[/tex][tex]T(0)=77[/tex]bi) We are to replace t with 12:[tex]T(12)=55(0.913)^{12}+22[/tex]Just put right hand side into the calculator as:55*(0.913)^12+22 which should output 40.45066 approximately.bii) We are to replace t with 36:[tex]T(36)=55(0.913)^{36}+22[/tex]Putting right hand side into calculator as 55*(0.913)^36+22 gives:24.0764 approximately.