Question

The population of a town grows at a rate proportional to the population present at time t. the initial population of 500 increases by 15% in 10 years. what will be the population in 40 years? (round your answer to the nearest person.) persons how fast is the population growing at t = 40? (round your answer to two decimal places.) persons/yr

Answer 1

The population is multiplied by 1.15 in a decade. After 4 decades it will be multiplied by 1.15^4, so will be 875 persons.

In terms of persons per year, you have
.. p(t) = 500*1.15^(t/10)
.. p'(t) = 500*(1/10)*ln(1.15)*1.15^(t/10) ≈ 6.988097*1.15^(t/10)
so
.. p'(40) = 12.22 . . . . persons/yr