From 1990 to 2006, the population, p (in millions), of a large city can be modeled by p = 1.1(1.05)t, where t is the number of years since 1990.
Incomplete.
I think you mean
p = 1.1(1.05)^t
Now just plug in various values for t and p to answer questions.
For example, after 7 years (1997)
p = 1.1 * 1.05^7 = 1.55
How long will it take p to grow by 46%?
1.1*1.46 = 1.1 * 1.05^t
1.05^t = 1.46
t = log(1.46)/log(1.05) = 7.76
The given equation is a model that represents the population of a large city over time from 1990 to 2006. To understand how the population is modeled, let's break down the equation:
p = 1.1(1.05)t
Here, p represents the population of the city and t represents the number of years since 1990. The equation can be interpreted as follows:
1. The term (1.05)t represents the exponential growth of the population over time. The base, 1.05, represents an annual growth rate of 5%. So, for each year that passes (t increases by 1), the population increases by 5%.
2. Multiplying this growth rate by 1.1 scales the population even further. The factor 1.1 accounts for additional factors such as immigration, birth rate, and other influences that cause the population to grow faster than the base growth rate of 5%.
By plugging in different values of t into the equation, we can calculate the estimated population for each corresponding year. For example, if we want to find the population in the year 2000, we substitute t = 10 into the equation:
p = 1.1(1.05)10
Using a calculator, we can compute this expression to find the estimated population for the year 2000.