Exponentials

Hong Kong

Stage 4 - Stage 5

Consider the plotted points.

Loading Graph...

a

Complete the table of values for the given points.

$x$x |
$1$1 | $2$2 | $3$3 | $4$4 |
---|---|---|---|---|

$y$y |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

b

Identify the common ratio between consecutive $y$`y` values.

c

State an equation relating $x$`x` and $y$`y`.

Easy

Approx 2 minutes

Consider the given table of values.

Find the equation of the curve in the form $y=a^x$`y`=`a``x`.

The graph of $f\left(x\right)=9^x$`f`(`x`)=9`x` is given below. Another exponential function, $g\left(x\right)$`g`(`x`), is increasing at exactly the same rate as $f\left(x\right)$`f`(`x`), but has a different $y$`y`-intercept. Which of the following could be the equation of function $g\left(x\right)$`g`(`x`)?

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