Question

The data in the table shows the population growth of a city since the year 2000. What kind of function models the data? How do you know?

Answer 1

According to the given table, the population doubles up each year, which means the data models geometric sequences which factor is 2, its first term is 5275. Let's find the function using a geometric sequence rule-

`f(x)=a_0\cdot(r)^(x-1)`

Replacing the given information, we have

`f(x)=5275\cdot(2)^(x-1)`

Hence, the function that models the data is exponential, as shown above.