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Every year 39 million cars cross the Golden Gate Bridge in San Francisco.
Which kind of function best models the relationship between time and the cumulative number of cars that have crossed the Golden Gate Bridge?
Choose 1 answer:
(A) Linear
(B) Exponential

Every year $39$ million cars cross the Golden Gate Bridge in San Francisco. $\newline$ Which kind of function best models the relationship between time and the cumulative number of cars that have crossed the Golden Gate Bridge? $\newline$ Choose $1$ answer: $\newline$ (A) Linear $\newline$ (B) Exponential

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Identify linear and exponential functions from word problem

Full solution

Q. Every year

39

million cars cross the Golden Gate Bridge in San Francisco.

\newline

Which kind of function best models the relationship between time and the cumulative number of cars that have crossed the Golden Gate Bridge?

\newline

Choose

1

answer:

\newline

(A) Linear

\newline

(B) Exponential

Problem Description: The problem is asking us to determine the type of function that would best describe the relationship between time and the cumulative number of cars crossing the bridge. To do this, we need to understand the characteristics of linear and exponential functions.
Characteristics of Linear Functions: A linear function is one where the rate of change is constant. This means that for each unit of time that passes, the same number of cars would cross the bridge. In this case, if $39$ million cars cross the bridge every year, then the cumulative number of cars would increase by $39$ million each year.
Characteristics of Exponential Functions: An exponential function, on the other hand, is one where the rate of change is not constant and the quantity increases by a certain percentage or factor over equal increments of time. This would mean that the number of cars crossing the bridge would not just increase by a fixed number each year, but rather by a percentage of the previous year's total.
Determining the Type of Function: Since the problem states that $39$ million cars cross the bridge every year, this suggests a constant rate of change. Therefore, the cumulative number of cars would increase by a fixed amount each year, which is characteristic of a linear function.

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