Question

Which of the following relationships, linear or exponential, will produce a greater output in the long run, and why?

A) Linear, because it grows steadily and predictably.
B) Exponential, because it grows at an accelerating rate.
C) Linear, because it starts with a larger initial value.
D) Exponential, because it is more sustainable over time.

Answer 1

An exponential relationship will produce a greater output over time because it grows at an accelerating rate, with the growth rate increasing as the population or value becomes larger.

Step-by-step explanation:

The question is focused on comparing linear and exponential relationships to determine which will produce a greater output in the long run. When considering long-term growth, an exponential relationship (B) will produce a greater output than a linear one, because it grows at an accelerating rate. An exponential function, such as bacterial growth under ideal conditions, has a growth rate that increases as the number of bacteria increases. This is contrary to a linear function, which grows by the same amount in each time step.

Therefore, the correct answer is B) Exponential, because it grows at an accelerating rate. While linear growth adds a constant amount to the output over equal increments of time, exponential growth multiplies the output by a constant factor over equal increments of time, leading to a rapidly increasing output as time goes on.

The correct option is B) Exponential, because it grows at an accelerating rate.