Limit of Crystal Growth Furnace

[Kaleb]

Homework Statement

A crystal growth furnace is used in research to determine how best to manufacture crystals used in electric components for the space shuttle. For proper growth of the crystal, the temperature must be controlled accurately by adjusting the input power. Suppose the relationship is given by the following equation, where T is the temperature in degrees Celsius and w is the power input in watts.
T(w) = 0.1w2 + 2.157w + 20

(a) How much power is needed to maintain the temperature at 197°C? (Give your answer correct to 2 decimal places.) X watts

(b) If the temperature is allowed to vary from 197°C by up to ±1°C, what range of wattage is allowed for the input power? (Give your answer correct to 2 decimal places.)
X watts (smaller value)
X watts (larger value)

The Attempt at a Solution

I am working this out on paper as I type this. My thought is that I find the w value to make the equation true? All I am looking for on this one is a hint, not the solution. NEED TO FIGURE OUT ON OWN! But, some guidance is always appreciated; any and all.

 

[HallsofIvy]

Homework Statement

A crystal growth furnace is used in research to determine how best to manufacture crystals used in electric components for the space shuttle. For proper growth of the crystal, the temperature must be controlled accurately by adjusting the input power. Suppose the relationship is given by the following equation, where T is the temperature in degrees Celsius and w is the power input in watts.
T(w) = 0.1w2 + 2.157w + 20

Can I presume that you mean T(w)= 0.1 w²+ 2.157w+ 20?

(a) How much power is needed to maintain the temperature at 197°C? (Give your answer correct to 2 decimal places.) X watts

(b) If the temperature is allowed to vary from 197°C by up to ±1°C, what range of wattage is allowed for the input power? (Give your answer correct to 2 decimal places.)
X watts (smaller value)
X watts (larger value)

The Attempt at a Solution

I am working this out on paper as I type this. My thought is that I find the w value to make the equation true? All I am looking for on this one is a hint, not the solution. NEED TO FIGURE OUT ON OWN! But, some guidance is always appreciated; any and all.

(a)If you want T(w)= 197, then replace T(w) in T(w)= 0.1w²+ 2.157w+ 20: Can you solve the equation 197= 0.1 w²+ 2.157w+ 20? Do you know the quadratic formula?

(b)If the temperature may be as high as 197+ 1= 198, you need to solve 198= 0.1w²+ 2.157w+ 20. If it can be as low as 197- 1= 196, you need to solve 196= 0.1w²+ 2.157w+ 20.

 

[Kaleb]

Yea, that is what I meant. My apologies for not proof reading. I did come up with 32.65 without(ironically) having to use the quad formula by an educated guess on the wattage. Thanks again for your tips, your an asset to this forum! I am glad that I was on the right track, and that your tips provided further evidence to this effect.

-Much appreciated,
Kaleb