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The number of visitors to the Eiffel Tower in Paris increases by
1.5% each year.
Which kind of function best models the relationship between time and the number of visitors to the Eiffel Tower?
Choose 1 answer:
(A) Linear
(B) Exponential

The number of visitors to the Eiffel Tower in Paris increases by $1.5\%$ each year. $\newline$ Which kind of function best models the relationship between time and the number of visitors to the Eiffel Tower? $\newline$ Choose $1$ answer: $\newline$ (A) Linear $\newline$ (B) Exponential

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Identify linear and exponential functions from word problem

Full solution

Q. The number of visitors to the Eiffel Tower in Paris increases by

1.5\%

each year.

\newline

Which kind of function best models the relationship between time and the number of visitors to the Eiffel Tower?

\newline

Choose

1

answer:

\newline

(A) Linear

\newline

(B) Exponential

Understanding the increase: Understand the nature of the increase in the number of visitors. $\newline$ The number of visitors increases by a certain percentage each year. This means that each year, the number of visitors is multiplied by a factor that is greater than $1$ . This is characteristic of exponential growth, where a quantity increases by a fixed percentage over equal intervals of time.
Comparing linear and exponential functions: Compare the characteristics of linear and exponential functions. $\newline$ A linear function increases by a fixed amount each period, while an exponential function increases by a fixed percentage each period. Since the number of visitors increases by a fixed percentage ( $1.5\%$ ), this suggests an exponential function rather than a linear one.
Choosing the correct answer: Choose the correct answer based on the analysis. $\newline$ Since the increase is by a fixed percentage, the kind of function that best models the relationship between time and the number of visitors to the Eiffel Tower is an exponential function.

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