Question

The population of a community was 200 people 10 yrs ago. Today the population is 550 people. Using an exponential growth function when will the population be 1000?

Answer 1

in 6 years

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.