Verified answer

33,000,000,000=4,281,000e^.025t

Dividing both sides by 4281000,

7708.479 = e^.025t

Taking the natural log of both sides,

ln 7708.479 = 0.025t

t = (ln 7708.479)/0.025

t = 358.003

33,000,000,000=4,281,000e^.025t

First divide both sides by

4,281,000

Which gives

7708.47932726 = e^.025t

Now take the natural log of both sides

ln7708.47932726 = lne^.025t

And since lne = 1 we now have

ln7708.47932726 = .025t

And so divide both sides by 0.25 to get

ln(7708.47932726)/(.025) = t

And plugging into calculator we get

358.003048531 = t

And you can round off as needed

:)

Let Po = Q (to make it easier to follow/read)

P = Qe^(kt)

P/Q = e^(kt)

ln(P/Q) = kt

ln(P/Q)/k = t

ln(P/Po)/k = t

Substitute in the values you have, and then evaluate to find t.

Remember that ln is the natural log.

t = ln(33000000000/4281000) / 0.025 = 358 (to 3 sig. fig.)