Exponentials

Hong Kong

Stage 4 - Stage 5

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

Loading Graph...

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

d

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

The linear function

A

The exponential function

B

Easy

Approx 2 minutes

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

Several points have been plotted on the number plane.

Consider the following table of values for the functions for $x\ge1$`x`≥1:

$f\left(x\right)=\left(1.05\right)^x$`f`(`x`)=(1.05)`x` and $g\left(x\right)=5x$`g`(`x`)=5`x`.

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