New Zealand
Level 8 - NCEA Level 3

# Comparing Exponential Models

## Interactive practice questions

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 $n$nth term in the sequence.

b

Write a formula for $g\left(n\right)$g(n), the $n$nth 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.

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.

### Outcomes

#### M8-7

Form and use trigonometric, polynomial, and other non-linear equations

#### 91575

Apply trigonometric methods in solving problems