Question

Please help this question.

Answer 1

Answer:

a). 59.049°C

b). 2.1179 seconds

Step-by-step explanation:

Expression representing the final temperature after decrease in temperature of the metal from 100°C to T°C is,

T = $100(0.9)^{x}$

where x = duration of cooling

a). Temperature when x = 5 seconds

T = 100(0.9)⁵

  = 59.049

  ≈ 59.049°C

b). If the temperature of the metal decreases from 100°C to 80°C

Which means for T = 80°C we have to calculate the duration of cooling 'x' seconds

80 = $100(0.9)^{x}$

0.8 = $(0.9)^{x}$

By taking log on both the sides

log(0.8) =log[$(0.9)^{x}$]

-0.09691 = x[log(0.9)]

-0.09691 = -0.045757x

x = $\frac{0.09691}{0.045757}$

x = 2.1179

x ≈ 2.1179 seconds