1. The problem states that the population of a town is modeled by the exponential function $$p(t) = 31,790 \times (0.95)^t$$ where $t$ is the number of years since 2010. 2. The initial population is the value of $p(t)$ when $t=0$ (the year 2010). Substitute $t=0$ into the function: $$p(0) = 31,790 \times (0.95)^0 = 31,790 \times 1 = 31,790$$ So, the initial population in 2010 was 31,790. 3. The population changes by a factor of 0.95 each year. Since 0.95 is less than 1, the population is decreasing. 4. The rate of change per year is found by subtracting 1 from the base of the exponent: $$0.95 - 1 = -0.05$$ This means the population decreases by 5% per year. Final answers: - The initial population of the town in 2010 was 31,790. - The population is decreasing at a rate of 5% per year.