Question

Quick help! Exponential modelling
The temperature (T) of a dish t minutes after it is removed from the microwave, is given by:

$T(t) = 55 \times ({0.913})^{t} +22°C$

a) What is the initial temperature of the dish?

b) What is the temperature after,
(i) 12 minutes

(ii) 36 minutes​

Answer 1

Answer:

a) 77 degrees Celsius

bi) 40.45066 degrees Celsius

bii) 24.0764 degree Celsius

Step-by-step explanation:

I'm assuming the temperature function is:

$T(t)=55(0.913)^t+22$.

a) The initial temperature can be found by replacing t with 0.

$T(0)=55(0.913)^0+22$

$T(0)=55(1)+22$

$T(0)=55+22$

$T(0)=77$

bi) We are to replace t with 12:

$T(12)=55(0.913)^{12}+22$

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:

$T(36)=55(0.913)^{36}+22$

Putting right hand side into calculator as 55*(0.913)^36+22 gives:

24.0764 approximately.