URGENT! Need math help fast!

[Hawkmoon]

Trying to help my newly-adopted daughter adapt to math class in the U.S. -- in English (she speaks Spanish and is just learning English). There's a problem on the homework sheet that doesn't make sense to me and I'm hoping some of you math geniuses can help me out.

The problem:

For the period 1991 to 2001, the number y (in millions) of Internet users worldwide can be modeled by the function y = 4.67(1.65)^x where x is the number of years since 1991.

a. Identify the number of Internet users worldwide there were in 1991.

b. Graph the function, then use the graph to estimate the year in which the number of users was about 21 million.

It's been a long time since I was a math/physics major, but I'm pretty sure I remember that you can't raise a number to a power of zero. Which would mean that part (a) of the question has no answer, because 1991 is zero years since 1991. Am I mis-remembering?

Thanks. Please answer as quickly as possible. It's 8:00 p.m. here on the right coast and the kid will be heading to slumberland before too long.

[Angel Eyes]

(any real number)⁰ = 1

[Hawkmoon]

Ah.

Thanks. That makes things a lot easier. I was somehow thinking it was infinity.

[lee n. field]

then use the graph to estimate the year in which the number of users was about 21 million.

I would guess that number would have been the case, worldwide, in 1991.  "Teh Internet" =/= "www".  There was plenty going on then.

[drewtam]

I think this is right. I'm a little rusty...

y(x) = 4.67*1.65^x

y/4.67 = 1.65^x

ln(y/4.67) = ln (1.65^x)
ln(y/4.67) = x * ln(1.65)

x(y) = ln(y/4.67)/ln(1.65)

x(21) = ln(21/4.67)/ln(1.65) =~ 3yrs => 1994

[GigaBuist]

Using a TI-83 emulator and graphing the function I confirm what drewteam says about the answer to the 2nd part.  It was about 1994.

Hit the Y= button and enter the formula.
Hit the 'Window' button and change the graph to show min X = 0, max X = 10, min Y = 0, max y = 25, hit graph, then trace, move the cursor around and you'll see it hit 21 on the Y coordinates just after you get beyond 3 on X.

[HankB]

a) 4.67 million

b) Using Excel's Solver I get Jan 24, 1994.

[Balog]

Not a math whiz, but good job on adopting. My wife and I are looking into that, as we've finally achieved a financial stability where it's feasible. I always love seeing people adopt.

[S. Williamson]

Bacon.

[drewtam]

Bacon.

I see your bacon, and raise you detcord.

[wuluf]

           2
(bacon)

[Angel Eyes]

(bacon)^bacon

[Hawkmoon]

It's astonishing how virtually any thread here that doesn't eventually evolve (or devolve) into detcord, seems to eventually involve bacon.

How to combine the two? Hmmm ...

What's the fastest way to cook bacon?

Detcord, of course.

[S. Williamson]

That'd be:

f(detcord) = bacon^bits

[280plus]

6 7/8