Jodi poured herself a cold soda that had an initial temperature of 45degreesF and immediately went outside to sunbathe where the

Question

3 years ago

5

Jodi poured herself a cold soda that had an initial temperature of 45degreesF and immediately went outside to sunbathe where the

temperature was a steady 101degreesF. After 8 minutes the temperature of the soda was 55degreesF. Jodi had to run back into the house to answer the phone. What is the expected temperature of the soda after an additional 10 minutes?

Mathematics

1 answer:

arlik [135] · Answer 1 · 2022-08-04T12:14:14+03:00

The initial temperature difference of 101-45 = 56 degees declined to 101-55 = 46 degrees in 8 minutes, We can write the exponential equation for the soda's temperature as

... T = 101 -56(46/56)^(t/8) . . . . where t is in minutes

After an additional 10 minutes, we have t=18, so the soda temperature will be

... T = 101 -56(46/56)^(18/8) ≈ 65.0 . . . degrees