Suppose the population of a town is 9,800 and is growing 2% each year. Write an equation to model the population growth. Predict the population after 7 years.
To model the population growth, we can use the equation:
P(t) = P₀ * (1 + r)^t
where P(t) is the population at time t, P₀ is the initial population, r is the growth rate (expressed as a decimal), and t is the time in years.
Given that the initial population (P₀) is 9,800 and the growth rate (r) is 2% or 0.02, the equation becomes:
P(t) = 9,800 * (1 + 0.02)^t
To predict the population after 7 years, we replace t with 7:
P(7) = 9,800 * (1 + 0.02)^7
Simplifying this expression will give us the estimated population after 7 years.