Question

The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population P0 has doubled in 5 years. Suppose it is known that the population is 8,000 after 3 years. What was the initial population P0? (Round your answer to one decimal place.) P0 = What will be the population in 10 years? (Round your answer to the nearest person.) persons How fast is the population growing at t = 10? (Round your answer to the nearest person.) persons/year

Answer 1

5278.0

21112

2927

Explanation:

P = Po[2^(t/5)]

8000 = Po(2^⅗)

Po = 5278.0

P = 5278(2^(10/5))

P = 21112

P = Po[2^(t/5)]

ln(P/Po) = (t/5)ln2

ln(P) - ln(Po) = (t/5)ln2

1/P . dP/dt = ln2/5

dP/dt = P(ln2)/5

At t = 10, P = 21112

dP/dt = 2927