2.22 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.
Write an equation for $M$M, Mohamad’s salary in $t$t years time.
Write an equation for $P$P, Elizabeth’s salary in $t$t years time.
How much greater will Elizabeth's salary be in $6$6 years' time than Mohamad's? Give your answer correct to the nearest cent.
Over the long term, whose salary will increase more rapidly?
Mohamad's
Elizabeth's
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 $3%$3% per year compounded annually, while Bank B offers a the same interest rate per year with interest compounded monthly.