(70/(2+4e^.2t))=20 solve for t?

Answer 1

70= 40 + 80e^.2t
30= 80e^.2t
3/8 = e^.2t
ln (3/8) = .2t
{by equivalent form which says the log base e of e^x = x}

ln (3/8) /.2 = t
t is approx. equal to -4.904146265

Answer 2

do the cross mulplication and you will get

2 + 4e^.2t = 70/20

transpose the number 2 to the right

4e^.2t = 7/2 - 2
4e^.2t = 3/2

divide both sides by 4

e^.2t = 3/8

take the ln of both sides .2t ln e = ln 3/8
.2t = ln 3/8
.2t = -.980829253

divide both sides by .2 you will get ( ln 3/8 ) / .2

t = -4.90414665

Answer 3

70/(2 + 4e^(.2t)) = 20
70/(2(1 + 2e^(.2t))) = 20
35/(1 + 2e^(.2t)) = 20
1 + 2e^(.2t) = (35/20)
1 + 2e^(.2t) = (7/4)
4 + 8e^(.2t) = 7
8e^(.2t) = 3
e^(.2t) = (3/8)
.2t = ln(3/8)
t = (ln(3/8))/(.2)
t = (10ln(3/8))/2
t = 5ln(3/8)

ANS : t = 5ln(3/8) or 5(ln3 - ln8)