Question

help with log word problem

Answer 1

You need to determine k from the initial change in temperature of the coffee, then use that k in the formula to find how long it will take to reach 180.

As a quick estimate, note that it dropped 10 degrees in ten minutes and you are asked to predict how long it will take to drop another 20 degrees, which should not be very different from 20 minutes, but that is an estimate. "How long" may mean
from t=0 or from t=10, not so clear wording.

Get k from

200 = 68 + (210 - 68) exp(-10 k)

[(200-68)/(210-68)] = exp(-10 k)

ln [ ] = - 10 k.

k = - (ln [ ])/10

Use that k in T = 68 + (210-68) exp(- k t)

and do the same thing as before, getting T.

I think the answer is B and that they are starting from t=0, but it could be C, starting from t=10, so check my calculations. Rule out A and C.

Alternatively, use the equation with the t options given and see which one works to predict T = 180.