Q:

Which of the choices below follow an exponential pattern? Select all that apply.

Accepted Solution

A:
Answer:The choices that follow an exponential pattern is:               A.  Division of skin cells every half hour.               C.  $$y=4\cdot 3^x$$Step-by-step explanation:We know that an exponential function is one which gradually increases or decreases by a constant rate.A)        Division of skin cells every half hour.It will determine a exponential pattern since it could be represented in the form of:          $$y=ab^x$$where a is the initial amount of skin cells and also the number of skin cells  decreases by a constant rate in every half hour.Hence, option: A is correct. B)               $$y=x^2$$It is not a exponential function.It is a quadratic function.Hence, option: B is incorrect.C)             $$y=4\cdot 3^x$$It is a exponential function.Since it is represented in the form of:       $$y=ab^x$$Hence, option: C is correct.D) From the given table we could see that this represent a linear function and not exponential since the values are increasing by a fixed rate i.e. 3Hence, option: d is incorrect.E)     You are driving at a constant rate of 55 mph.This situation will represent a linear function or we may say a constant function.  Hence, option: e is incorrect.F)           $$y=2x^3$$It represent a cubic function and not exponential.Hence, option: F is incorrect.