Final answer:
The population of Blueville, starting at 7000, with a growth rate of 1.4% per year, can be represented by the exponential growth function P(t) = 7000 × (1 + 0.014)^t, where P(t) is the population at time t.
Step-by-step explanation:
To represent the population of Blueville as a function of time with an initial population of 7000 and an annual growth rate of 1.4%, we can use the exponential growth model. This mathematical model is commonly used in demography to estimate population changes over time. The standard form of this model is:
P(t) = P0 × (1 + r)t
Where:
- P(t) is the population at time t
- P0 is the initial population
- r is the annual growth rate (expressed as a decimal)
- t is the time in years
For Blueville:
- P0 = 7000 people
- r = 0.014 (since 1.4% = 0.014)
- t will be the number of years since the growth began
Thus, the function representing the population growth over time in Blueville is:
P(t) = 7000 × (1 + 0.014)t
Using this function, one can calculate the population of Blueville for any given year, by plugging in the value of t into the equation.