Write a function in terms of t that represents the situation.
1 answer:
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Answer:
f(x) =
Step-by-step explanation:
First we identify the Vertical Asymptote. Which is at x = 2
The function has a VA only at the point where the denominator gives 0, so because we know x = 2 is the VA, the denominator will be x - 2.
Then we identify the Horizontal Asymptote, which is the behavior of the function for very large 'x', or the horizontal line of the graph on the y - axis. Which is at y = 1. So our function will go to 1, as x grows incredibly large.
But since our denominator is x - 2, the top remains 1, but we should add a 1 to the function so it really has a HA at y = 1.
f(x) =
Answer:
a
f'(t) is negative
b
The unit is degC/min
c
At <u>35</u> minutes after the coffee was put on the counter, its temperature is <u>68</u> and will <u>decrease</u> by about <u>0.75</u> in the next 30 seconds.
Step-by-step explanation:
From the question we are told we are told that
The equation for the temperature of a cup of coffee place on a counter is
Here t is the time in minutes the coffee was put on the counter
Generally f(t)' is the derivative of f(t) at it represents the change of the temperature of the cup of coffee with respect to time
Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence f(t)' is negative
Generally the unit of the temperature is in degrees Celsius while that of time is in minutes
So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e degC/min)
From the question we are told that
i.e the rate of change of temperature after 35 minutes is 1.5
and
i.e the temperature of the cup of coffee after 35 minutes is 67 degC
Now after another t= 30 seconds = the rate of change of the temperature of the cup of coffee is
=>
=>
So
At <u>35</u> minutes after the coffee was put on the counter, its temperature is <u>68</u> and will <u>decrease</u> by about <u>0.75</u> in the next 30 seconds.