The equation that represents a population of 10,000 growing at a rate of 5% per year can be written as:
P(t) = P₀ * (1 + r)^t
Where:
P(t) represents the population at time t
P₀ represents the initial population (10,000 in this case)
r represents the growth rate (5% or 0.05 as a decimal)
t represents the number of years
Using this equation, we can calculate the population at different time points and create a graph to visualize the growth. Let's consider a time period of 10 years:
P(t) = 10,000 * (1 + 0.05)^t
To create a graph, we can plot the population (P) on the y-axis and the time (t) on the x-axis. Here's an example graph:
This graph will show the population starting at 10,000 and increasing exponentially over time with a growth rate of 5% per year.