Malthusian models have the following form:

P(t) = P0*e^(rt) , where

P0 = 70,000 is the initial population size,

the population is expected to double every 9 years:

for t = 9 years we have P = 2 P0 or

2 P0 = P0 * e^(9r) divid eboth sides by Po

e^(9r) = 2

9r = ln 2

r = (1/9) ln 2

P(t) = 70,000*e^(((1/9) ln 2)t)

we nee to find t such that P = 1,000,000 that is

70,000*e^(((1/9) ln 2)t) = 1,000,000 divide both sides by 70,000

(e^(ln 2))^((1/9)t) = 10/7

2^((1/9)t) = 10/7

(1/9)t = (log(10/7))/(log 2)

t = 9* (log(10/7))/(log 2)

t = 4.63 years

click here to see the step by step solution of the equation:

in 4.63 years the population will reach one million.