B(t) = 4*e^0.8t
remember that ln(e)=1 and log(a^b)=b(log(a))
solve for value of t such that B(t)=100
so
100=4*e^0.8t
divide both sides by 4
25=e^0.8t
take ln of both sides
ln(25)=ln(e^0.8t)
ln(25)=0.8t(ln(e))
divide both sides by 0.8
ln(25)/0.8=t(1)
ln(25)/0.8=t
t=ln(25)/0.8
t≈4.02359
so about 4 years
answer is C
