Explore how repeated multiplication generates exponential growth or decay in tables of values. Recognize growth factors by comparing outputs.
[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]
A table of values for a function [math]y=f\left(t\right)[/math] contains two consecutive values of [math]t[/math] and the corresponding values of [math]y[/math].[br]Is this data enough to decide whether the table represents an exponential growth or decay function? [br]If not, what is the minimum number of data pairs that you need?
A table of values representing the ordered pairs [math]\left(t,y\right)[/math], where [math]y=f\left(t\right)[/math], shows that as [math]t[/math] increases by 1, [math]y[/math] is multiplied by 3.14. [br]Can you classify this function as an exponential one?[br]If so, write a possible equation for this function, using a form that shows the growth or decay factor.