Unit 2 CF/CU

The graph shows two investment models. Model 1 is compounding annually, while Model 2 increases linearly by $126 per year. See diagram.

Determine the difference between the two investment strategies in 2030, to the nearest dollar.

The least-squares line for a sample of five data points was found to be y = 2.1875x + 0.0625, with a correlation coefficient of r = 0.875.

Determine a set of values for p and q, given that these values differ by 3.

• 𝑝=12

  𝑞=15

• 𝑝=15

  𝑞=12

• p=40

  q=43

• p=43

  q=40

The table shows the total number of times a new song is played on a music service in the days following its first release. The songwriter is paid 0.175 cents every time their song is played and will be paid after 60 days. They

predict that by that time, they will be owed at least $1000.

Given that the number of times the song is played is increasing exponentially, evaluate the reasonableness

of this prediction.

The number of people living in each household and the average daily household water usage, measured in litres (L), were recorded for 10 households.

Calculate Pearson’s correlation coefficient

From the previous question, would the correlation coefficient of 0.886 be appropriate for the association between daily water usage and the number of people living in a household.

See diagram to assist in decision.

• yes

• no

Reasoning for the previous question.

From the calculator 𝑟 = 0.886

A correlation coefficient of 0.886 indicates that the relationship is a very strong positive relationship.

However, this relationship as shown in the scatterplot does not appear to be linear, therefore the correlation coefficient should not be used.

Do you agree?

• yes

• no