i cant figure out this problem i get so close but i'm doing somthing wrong

Question

g = 4.5 e^(0.2 t). When g=4, find t.

Answer 1

To solve this you will need to solve for t by applying the same operations to both sides of the equation.  I this case, you divide by 4.5, then take the natural log, then divide by 0.2.  You will also have to substitute for g.

Start with:  g = 4.5 e^(0.2 t)

Then divide by 4.5:  g/4.5 = e^(0.2 t)

Then take the natural log: ln(g/4.5) = 0.2 t

Then divide by 0.2: t = [ln(g/4.5)] / 0.2

Then substitute for g:  t = [ln(4/4.5)] / 0.2

Plug into calculator and get:  -0.589   (this answer is rounded to three significant digits.)

Answer 2

to solve this, you have to do a lot of reverse calculations.

g = 4.5 e^.2t

4= 4.5 e^.2t

divide both sides by 4.5

.889 = e^.2t

take the natural log of both sides (ln)

-.1178 = .2t

divide both sides by .2

-.5889 = t