Question

Solve the following recurrence relations for the initial conditions given. The population of Utopia increases 5 percent per year. In 2000 the population was 10,000. What was the population in 1970?

Answer 1

$$P(t)=P_0(1+r)^t$$

Given $r=0.05, P(30)=10000$

$$P_0=\dfrac{P(30)}{(1+r)^{30}}=\dfrac{10000}{(1+0.05)^{30}}=2314$$

The population was 2314 in 1970.