Question

The thermal plot of a gaming system during play time is defined by 10ln(15t^3) − 2T + 100 = T + 10t for 0 < t ≤ 5, where t represents time in hours and T represents temperature in °C. For which condition does the system reach a possible maximum or minimum temperature?

30 − 10t = 0
450t^2 − 10 = 0
6 − 90t^3 = 0
15t^2 − 10 = 0

Answer 1

(a) 30 -10t = 0

Explanation:

Given a relation between time (t) and temperature (T), you want to know the condition that will describe when T reaches an extreme.

10·ln(15t³) -2T +100 = T +10t

Extreme

The temperature T will be at an extreme when the derivative with respect to t is 0.

Simplifying the logarithm, we can write ...

10·(ln(15) +3·ln(t)) -2T +100 = T +10t

Differentiating with respect to t gives ...

10(0 +3/t) -2T' +0 = T' +10

Setting T' to zero, we have the equation ...

30/t = 10

30 = 10t . . . . . multiply by t

30 -10t = 0 . . . . matches choice A

<95141404393>