An airline charges £300 for a flight of 2000 km and £700 for a flight of 4000 km. (a) Plot these points with distance on the horizontal axis and cost on the vertical axis. (b) Assuming a linear model estimate (i) the cost of a flight of 3200 km. (ii) the distance travelled on a flight costing £400.

Graphs, equations and logarithms problems

1. Three companies can supply a university with some mathematical software. Each company has a different pricing structure:

Company 1 provides a site licence which costs £130,000 and can be used by anyone at the university.
Company 2 charges £1,000 per user.
Company 3 charges a fixed amount of £40,000 for the first 60 users and £500 for each additional user.

(a) Draw a graph of each cost function on the same set of axes.
(b) What advice can you give the university with 500 users about which company to use?

2. An airline charges £300 for a flight of 2000 km and £700 for a flight of 4000 km.

(a) Plot these points with distance on the horizontal axis and cost on the vertical axis.
(b) Assuming a linear model estimate
(i) the cost of a flight of 3200 km.
(ii) the distance travelled on a flight costing £400.

3. Monthly sales revenue, R (in £), and monthly advertising expenditure, A (in £), are modelled by the linear relation, R = £9,000 + 12A.

(a) If the firm does not spend any money on advertising what is the expected sales revenue that month?
(b) If the firm spends £800 on advertising one month what is the expected sales revenue?
(c) How much does the firm need to spend on advertising to achieve monthly sales revenue of £15,000?
(d) If the firm increases monthly expenditure on advertising by £1 what is the corresponding increase in sales revenue?

4. Solve the following equations

(a)
(b)
(c)
(d)
(e),
(f) .

5. Simplify the expression

.

6. During a recession a firm’s revenue declines continuously so that the revenue, R (measured in millions of pounds), in t years’ time is modelled by

(a) Calculate the current revenue and also the revenue in 2 years’ time.
(b) After how many years will the revenue decline to £2.7 million?

7. Plot and find the roots of the quadratic, . Write the quadratic as a product of two factors.

8. Find the points of intersection of the two curves, and , by plotting them and analytically.

9. Attempt to solve the following system of equations and comment on the result.

(a) (b)

10. Solve the system of 3 equations

Last Completed Projects