Well assuming an exponential model

A(t) = A_0 * exp{bt}

At t = 0 we have

A(0) = 24 * exp(b * 0} = 24

So

A(t) = 24 * exp{bt}

In 1950 we have t = 1950 - 1859 = 91

So

600 000 000 = 24 * exp{91t}

Divide both sides by 24 and take the natural log of both sides:

91t = ln(25 000 000)

Now solve for t.

As for can the rate keep up, what is A(92)? A(93)? Do these numbers make sense?

-Dan