Exponential vs. linear models

Question

The number of visitors to the eiffel tower in paris increased by 1.5% each year. Which kind of function best models the relationship between time and the number of visitors to the eiffel tower?

Answer 1

The best type of function for the relationship between time and the number of Eiffel tower visitors would be an exponential one. This is because we know that each year, the number of visitors increases by a percentage, not by a steady number. Each year, the number of people visiting is increased based on the previous year.

In order for this function to be linear, the number of visitors would have to increase by the same amount each year.

Imagine a linear equation like a staircase. As you go forward one step, you also go up by one step each time. This forward-one-step up-one-step situation would continue until you run out of stairs. An exponential equation would be more like going forward one step and then going up one step. The next time you go forward one step, you'd be going up two steps. The time after that, forward one step and up four steps with the number of steps you go upward doubling each time.

Eiffel tower visitors work the same way as the doubling-staircase scenario. Each year (or step forward), the number of people (or step up) increases by 1.5%. If one year there were 200 people, it would increase by 1.5% of that the next year and the number would be 203 people.