5.05 Comparing linear and exponential relationships
Interactive practice questions
A linear function and exponential function have been drawn on the same coordinate plane.
A Coordinate plane has its x-axis ranging from $0$0 to $5$5 and its y-axis ranging from $0$0 to $20$20. A linear function is plotted as a gray line on the Coordinate plane. The line starts at $\left(0,0\right)$(0,0) and moves upward to the right. The line passes through the point $\left(1,4\right)$(1,4) and extends beyond the visible part of the graph. An exponential function is plotted as a black curve on the same Coordinate plane. The curve starts at $\left(0,1\right)$(0,1) and moves upward to the right. The curve passes through the point $\left(1,2\right)$(1,2) and extends beyond the visible part of the graph. The points are not marked and the coordinates are not explicitly labeled or given.
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.