Find Gemma’s annual salary for the year 2021, to the nearest dollar.

Assuming Kaia’s annual salary can be approximately modelled by the equation $S=ax+b$, show that Kaia had a higher salary than Gemma in the year 2021, according to the model.

METHOD 1

using geometric sequence with $r=1.02$           (M1)

correct expression or listing terms correctly           (A1)

$45000\times 1.{02}^{10}$  OR  $45000\times 1.{02}^{11-1}$  OR  listing terms

Gemma’s salary is $\$54855$ (must be to the nearest dollar)           A1

METHOD 2

$N=10$

$\text{PV}=\mp 45000$

$\text{I}\%=2$

$\text{P/Y}=1$

$\text{C/Y}=1$

$FV=\pm 54854.7489\dots$           (M1)(A1)

Gemma’s salary is $\$54855$ (must be to the nearest dollar)           A1

[3 marks]

finds $a=1096.89\dots$ and $b=-2160753.8\dots$ (accept $b=-2.16\times {10}^6$)         (A1)(A1)

Note: Award (A1)(A1) for $S=1096.89\dots x+33028.49\dots$, or $S=1096.89\dots x+43997.4\dots$, or $S=1096.89\dots x+45094.3\dots$

Kaia’s salary in 2021 is $\$56063.21$ (accept $\$56817.09$ from $b=-2.16\times {10}^6$)           A1

Kaia had a higher salary than Gemma in 2021           AG

[3 marks]

Many errors were seen in part (a). Some candidates used the incorrect formula ${\left(1+\frac{0.02}{100}\right)}^{10}$ or used an incorrect value for the exponent e.g. 9 was often seen. Others lost the final mark for not answering to the nearest dollar.
Very few tried to make a table of values.

In part (b) students often let $x$ represent the number of years since a given year, rather than the year itself. Despite this, most were able to find the correct amount with their equation and were awarded marks as appropriate. Some students did not realise regression on GDC was expected and tried to work with a few given data points, others had difficulty dealing with the constant in the regression equation if it was reported using scientific notation.