Modeling Coffee Cooling: Temperature After 16 Minutes & Inverse Calculation

example two celest heated a cup of coffee and then let it cool to room temperature celest found the coffee's

temperature te measures in Celsius could be modeled by the volume function where T is the time in minutes

pay more attention to the units after the coffee started to cool find the coffee's temperature 16 minutes

after it started to cool check the units minutes minutes look at this function 16 minutes T =

16 so we just do the substitution T of 16 every single T will be changed into 16 71 * e to the

0.0514 * 16 power + 23 = 71 times e to the X power is this button do not use the the alphabet e

0.0514 time 16 power then plus 23 enter 54 two at the 36 fix or you write down the whole thing put the dot

dot dot for this T of for 16 if you are not good at this uh function notation you can just write down P

equal 71 * e to the 0.0514 * 16 power + 23 equal

54.2 the graph of T has a horizontal ASM toot line write down the equalent of the horizontal ASM to line we do know for

exponential function y = a * B to the X power + C then

horizontal ASM toot line is y = c so go back to this function we do know the constant number it's a

23 equation you have to write down y = 23 you cannot just write down 23 go to say write down the room

temperature we do know for this function 23 is the horizontal ASM toot line horizontal ASM toot line

means possible minimum value or maximum value because this horizontal ASM total means when T approaches

Infinity this temperature will approach

23 Celsius from this contest we could say the coffee will cool down to the room temperature which is

23 Celsius let's go to D given that inverse T of 50 equals K find the value of K let's go back to the concept of for

inverse function for inverse function of a equals B we will try to get rid of this

inverse function we will take a function f for both sides the

then function f and a inverse of function f will be cancelled we got a = f of B so for this

situation inverse T of 50 = k we will put a function T both sides then we

cancel we got 50 = T of K for T of T = 71 * e to the 0.0514 T the power +

23 then use the function notation T of K we will change this T into K 71 1 * e to the

0.0514 K plus 23 so we got this equation 50 = 71 * e to the power

of0 514 k+ 20 2

3 by solver we will type the whole equation into this

function then control menu enter enter enter K = 18.8 so k = 18.8