A number plane with the axes labeled as x and y. x-axis ranges from 0 to 5 and y-axis ranges from 0 to 20. A straight line(a linear function, $ArbitraryFunction('4*x')$ArbitraryFunction(′4*x′)) and a curve line(an exponential function, $ArbitraryFunction('2**x')$ArbitraryFunction(′2**x′)) is plotted. (Do not mention the linear function and exponential function as these are not given in the image)

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

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

The linear function

The exponential function

Easy

2min

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.

Easy

1min

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.

Easy

1min

Consider the functions $f\left(x\right)=3x$f(x)=3x and $g\left(x\right)=3^x$g(x)=3x.

Easy

6min

Outcomes

I.F.LE.1

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

I.F.LE.1.a

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

I.F.LE.1.b

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

I.F.LE.1.c

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

I.F.LE.3

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly.

5.05 Comparing linear and exponential relationships

Interactive practice questions

Outcomes

I.F.LE.1

I.F.LE.1.a

I.F.LE.1.b

I.F.LE.1.c

I.F.LE.3

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