Answer:
in 6 years
Step-by-step explanation:
Using t=10 to represent today, we can write the exponential growth function as ...
p(t) = 200(550/200)^(t/10)
Then we can set p(t) = 1000 and solve for t:
1000 = 200(11/4)^(t/10) . . . . simplifying the growth factor
1000/200 = (11/4)^(t/10) . . . . divide by 200
log(5) = (t/10)log(11/4) . . . . . . take logs
t = 10·log(5)/log(11/4) ≈ 15.91
That is, about 16 years from 10 years ago, the population will reach 1000.
The population will reach 1000 in about 6 years.
