 5.05 Comparing linear and exponential relationships

Interactive practice questions

A linear function and exponential function have been graphed on the same coordinate axes.

a

Over a $1$1 unit interval of $x$x, by what constant amount does the linear function grow?

b

Over a $1$1 unit interval of $x$x, by what constant ratio does the exponential function grow?

c

Would it be correct to state that the linear function always produces greater values than the exponential function?

Yes

A

No

B

Yes

A

No

B
d

As $x$x approaches infinity, which function increases more rapidly?

The linear function

A

The exponential function

B

The linear function

A

The exponential function

B
Easy
Approx 2 minutes

Consider the following table of values for the functions for $x\ge1$x1:

$f\left(x\right)=5^x$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.

Outcomes

F.LE.A.1

Distinguish between situations that can be modeled with linear functions and with exponential functions.

F.LE.A.1.A

Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

F.LE.A.1.B

Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

F.LE.A.1.C

Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

F.LE.A.3'

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 'Linear and exponential