How do I calculate this to get more marks😭

Question

The mean hourly earnings y (in RM) of employees at outpatient care centers in Malaysia from 2015 to 2020 can be modeled by

y = 0.782t + 15.2 0 ≤ t ≤ 5

where t represents the year, with t = 0 corresponding to 2015. Illustrate the model to estimate the year in which the mean hourly earnings were RM16.75.

(20marks)

Answer 1

Hello Tengku,

You're looking to find in which year the mean hourly earnings were RM 16.75. To do that, you would

1. set the modeling equation equal to 16.75,
2. solve for t, and
3. add 2015 to get a year estimate

1. Set modeling equation equal to 16.75: 16.75 = 0.782t + 15.2
2. Solve for t: subtract 15.2 from both sides: 16.75 - 15.2 = 0.782t ---> 1.55 = 0.782t; Divide both sides by 0.782 ---> 1.55/0.782 = t ---> t = 1.982
3. Add 2015 to get a year estimate: why do you have to add 2015? Because the problem tells you t = 0 corresponds to 2015. So add 1.982 to 2015 = 2016.982 which you can round up to 2017.

Using the modeling equation, you can estimate 2017 as the year in which the mean hourly earnings were RM 16.75.