# 5.04 Comparing exponential relationships

## Interactive practice questions

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

a

Write an equation for $M$M, Mohamad’s salary in $t$t years time.

b

Write an equation for $P$P, Elizabeth’s salary in $t$t years time.

c

How much greater will Elizabeth's salary be in $6$6 years' time than Mohamad's? Give your answer correct to the nearest cent.

d

Over the long term, whose salary will increase more rapidly?

A

Elizabeth's

B

A

Elizabeth's

B
Easy
Approx 5 minutes

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.

Bank A pays interest at a rate of $5.3%$5.3% per year compounded annually, while Bank B offers a rate of $4%$4% per year with interest compounded quarterly.

### Outcomes

#### F.LE.B.5

Interpret the parameters in a linear or exponential function in terms of a context.