Exponentials

Hong Kong

Stage 4 - Stage 5

Consider the two number sequences.

$f\left(n\right)$`f`(`n`): $1$1, $3$3, $9$9, . . .

$g\left(n\right)$`g`(`n`): $1$1, $2$2, $4$4, . . .

a

Write a formula for $f\left(n\right)$`f`(`n`), the $n$`n`th term in the sequence.

b

Write a formula for $g\left(n\right)$`g`(`n`), the $n$`n`th term in the sequence.

c

The sequence $f\left(n\right)$`f`(`n`) has been graphed. On the same axes, graph the first $4$4 terms of the sequence $g\left(n\right)$`g`(`n`) as ordered pairs on the number plane.

Loading Graph...

Easy

Approx 3 minutes

Mohamad has just started a new job, where his starting salary is $\$50000$$50000 p.a. and is expected to increase by $3.2%$3.2% each year. Elizabeth has also just started a new job, which has a starting salary of $\$49000$$49000 p.a. and is expected to increase at a rate of $6.1%$6.1% each year.

Switzerland’s population in the next $10$10 years is expected to grow approximately according to the model $P=8\left(1+r\right)^t$`P`=8(1+`r`)`t`, where $P$`P` represents the population (in millions) $t$`t` years from now.

The world population in the next $10$10 years is expected to grow approximately according to the model $Q=7130\left(1.0133\right)^t$`Q`=7130(1.0133)`t`, where $Q$`Q` represents the world population (in millions) $t$`t` years from now.

To investigate the environmental effect on bacterial growth, two colonies of the same bacteria were placed one in a constantly sunlit environment, the other in a dark environment. The graph shows the population of each colony after a certain number of days.

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