At 7 a.m., a colony of 100 bacteria is placed on a petri dish where the population is growing exponentially and will triple every 6 hours.

Select all statements that are true about the bacteria population.

The exponential function \(f\) is given by \(f(x) = 3^x\).

1. By what factor does \(f\) increase when the exponent \(x\) increases by 1? Explain how you know.
2. By what factor does \(f\) increase when the exponent \(x\) increases by 2? Explain how you know.
3. By what factor does \(f\) increase when the exponent \(x\) increases by \(\frac{1}{2}\)? Explain how you know. 

A piece of paper has an area of 93.5 square inches. How many times does it need to be cut in half before the area is less than 1 square inch? Explain how you know.

The area covered by an invasive tropical plant triples every year. By what factor does the area covered by the plant increase every month?