2.23 Comparing linear and exponential relationships
Interactive practice questions
A linear function and exponential function have been drawn on the same coordinate plane.
Over any $1$1 unit interval of $x$x, by what constant amount does the linear function grow?
Over any $1$1 unit interval of $x$x, by what constant ratio does the exponential function grow?
Would it be correct to state that the linear function always produces greater values than the exponential function?
Yes
No
As $x$x approaches infinity, which function increases more rapidly?
The linear function
The exponential function
Consider the following table of values for the functions for $x\ge1$x≥1:
$f\left(x\right)=5^x$f(x)=5x and $g\left(x\right)=2190x$g(x)=2190x.
Matt and Sophia are saving money using different strategies.
The amount each has saved after each month is given by the table of values and the plotted points.
Consider the functions $f\left(x\right)=3x$f(x)=3x and $g\left(x\right)=3^x$g(x)=3x.