Answer: A) Option B
B) 22.3 minutes.
Step-by-step explanation:
The temperature decreases in an exponential decrease, this means that we can write the equation as:
T(x) = A*r^x + B
Where A is the difference between the initial temperature and the room temperature, B is the room temperature, and r is a positive number smaller than 1, that says "how fast" the temperature decreases (and x is the variable, in units of time)
We know that the initial temperature
A = 200° - 72° = 128°
B = 72°
T(x) = 128°r^x + 72°
The only option with those two values is option B.
T(x) = 128(0.989)^x + 72
We should check that when x = 2m, the temperature must be 197°
T(2m) = 128*(0.989)^2 + 72 = 197.2° (that we can round down to 197°)
So this equation is correct
Now we want to find the time such the temperature is 172°F
then:
172° = 128°(0.989)^x + 72°
100° = 128°(0.989)^x
100/128 = (0.989)^x
x = ln(100/128)/ln(0.989) = 22.3 minutes.
Let's check in our equation:
T(22.3) = 128°(0.989)^22.3 + 72 = 172°
, the coefficient of the x² term is 1.