Question

Cedric bought a camera the year he started his job. The camera cost $41.40 at year 0. He notices the value of his camera decreases each year, at a rate of 8% per year.
Cedric sketches a graph of the situation.

Which statements are true?

Select each correct answer.



The graph has an x-intercept and a y-intercept.

The graph decreases from left to right.

The graph increases from left to right.

The graph has a y-intercept only.

The point (41.40, 0) is on the graph.

The point ​ (0, 41.40) ​is on the graph.

Answer 1

The point ​ (0, 41.40) ​is on the graph.The graph has a y-intercept only.The graph decreases from left to right.

Answer 2

Answer: The correct options are: 'The graph has an x-intercept and a y-intercept', 'The graph decreases from left to right' and 'The point ​ (0, 41.40) ​is on the graph'.

Explanation:

Let x represents number of years and y represents total cost of camera after x years.

Then, according to the given question,

$y=41.40-\frac{41.40\times 8\times x}{100}$

⇒$y=41.40-3.3120x$

Since if x=0, y=41.40 therefore function has y-intercept at (0,41.40)

And, if y=0, x=12.5 therefore function has an x-intercept at (12.5,0)

Since, the value of y is decreasing continuously therefore the graph of the function must be decreasing from left to right.

Thus, from the above explanation we can say that, option (1) , (2) and (6) are the correct options.