Question

N(t)=2000e^(1.1t)

the continuous growth rate is 110%

effective growth rate?__%

Q(t)=65e^(0.09t)
continuous growth rate is 9%
effective growth rate?__%

G(t)=650e^(0.055t)
continuous growth rate is 5.5%
effective growth rate?__%

round to 2 decimal places when necessary for effective growth rate...


is there a formula for effective growth rate

Answer 1

I will do the last one, you do the other two

G(t)=650e^(0.055t) , tells me the continuous rate is 5.5%

with a different base:
G(t) = 650(1+r)t

pick t = 5, (we can choose anything)
in the first:
g(5) = 650 e^(.055(5))
= 650 e^(.275) = 855.7449

in the 2nd:
855.7449 = 650(1+r)^5
1.316530675 = (1+r)^5
take 5th root of both sides

1.05654 = 1+r
r = .05654 -----> 5.654%