If a town with a population of 10,000 doubles every 14 years, what will the population be in 42 years and is it modeled by a linear function or a exponential function?

This is an exponential function.
The starting population is: 10,000 and it doubles every 14 years.
In 42 years ( 42 : 14 = 3 ) the population doubles 3 times.
The equation ( exponential ) is :
y = 10,000 * 2^n
In this case: n = 3
y = 10,000 * 2 ^3 = 10,000 * 8 = 80,000
In 42 years the population of this town will be 80,000.