Acold drink is taken from a cooler. initially, its temperature is 5°c. after 25 minutes in a 20°c room its temperature has increased to 10°c.

(a) what is the temperature of the drink after 45 minutes? (round your answer to two decimal places.)
12.77 °c (correct)

(b) when will its temperature be 14°c? (round your answer to two decimal places.)
56.56 minutes (incorrect)

(a) the temperature of the drink after 45 minutes is 12.77

(b) its temperature be 14 at t =  56.50 Minutes

Step-by-step explanation:

Given information:

Initial temperature, = 5

Sorrounding temperature, C = 20

in 25 minute, T(25) = 10

(a) the temperature of the drink after 45 minutes

According Newton's law of cooling

T(t) = C + ( - C)

where

= initial temperature

t = time

k = cooling constant

C = sorrounding temperature

Thus,

T(25) = 20 + (5 - 20)

10 = 20 - (15 )

=

-25k = ln()

k = - (ln())/25

  = 0.016

hence, the complete equation

T(t) = 20 + (5 - 20)

in 45 minute the temperature is

T(45) = 20 + (5 - 20)

T(45) = 12.77

the temperature is 14, so T(t) = 14

T(t) = 20 + (5 - 20)

14 = 20 + (5 - 20)

=

-0.016t = ln ()

t = - (ln ())/ 0.016)

t = 56.50 Minutes

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.