Subject: Question
Name: Brittany
Who are you: Student

A college math class consists of 32 students. On Monday at 9:00 a.m., the teacher tells one student to notify other students that the test scheduled for Wednesday at 9:00 a.m. has been cancelled. The model for the number of students in the class who will have heard this information after t hours is N=32-32e^-0.02t. After how many hours will the class have been notified?

Hi Brittany.

Since N=32-32e^-0.02t, you are asking when does N reach 32. Strictly speaking, it never does (if you put t=1000000 in there, you get a number very close to, but not quite, 32).

So the real problem is deciding when N is "close enough" to 32. That's a judgment call. Let's say that 31.5 is "close enough". Then the problem becomes this:

31.5 = 32-32e^-0.02t

which you can re-arrange to

(1/64) = e^-0.02t

Now to solve for t you need to get it out of the exponent. You can do that by taking the logarithm of both sides.

Hope this helps,
Stephen La Rocque.