FROM THE WORD PROBLEM HOW TO CHECK IF IT IS DISCRETE OR CONTINUOUS

Problem 1 :

A 20 gallon bathtub is draining at a rate of 2.5 gallons per minute. The number g of gallons remaining is a function of the number m of minutes. Is the domain discrete or continuous ?

Solution :

Original capacity of bathtub = 20 gallons.

It is draining at the rate of 2.5 gallons per minute.

Let g be the remaining quantity of water and m be the number of minutes.

g = 20 - 2.5m

Domain is continuous.

Problem 2 :

Are the data shown in the table discrete or continuous ? Explain.

Solution :

Number of stories will be only integer. So, the data is discrete.

Problem 3 :

The function m = 40 - 8.5 b represent the amount m of money (m) in dollars that you have after buying b balls of yarn. Graph the function using domain of 0, 1, 2 and 3. Is the domain discrete or continuous ?

Solution :

m = 40 - 8.5 b

Applying the given domain values one by one, we get

Here b represent number of balls. So, the domain is discrete.

Problem 4 :

The input of one function is length. The input of another function is number of shirts. Which function has continuous domain ? Explain.

Solution :

Length may has decimal values, for example 12.5 m,13 m are possible values. So, the input of this function is continuous.

Number of shirts must be integer values, for example 12 shirts 25 shirts are possible values. 13.5 shirts is not possible. So, the input of this function is continuous.

Problem 5 :

The function y = 3.25x converts length from x meters to y feet. Graph the function. Is the domain discrete or continuous.

Solution :

Here values of x may have decimals also. So, the domain is continuous.

Problem 6 :

Area A of the triangle is a function of the height h. Is the domain discrete or continuous ?

Solution :

Here h represents height of the triangle.

Area of triangle (A) = (1/2) x base x height

A = (1/2) x 8 x h

A = 4h

h may take decimals. So the function is continuous.

Problem 7 :

You are packing books into boxes. The function y = 20x represents the number y of books will fit into x boxes.

a) Is 4 in the domain ? Explain 

b) Is 60 in the range ? Explain

Solution :

y = 20x

x - number of boxes and y - number of books

a) Number of boxes may be 4. So, the value of x may be 4.

b) Checking if the range is 60,

60 = 20x

x = 60/20

x = 3 (number of boxes)

Since we get value of x as integer when y = 60, it  is possible  value for range.

Problem 8 :

You want to fill a 2 foot shelf with framed pictures. There are x pictures in 4 inch frames and y pictures in 8 inch frames 

a) Write the function for this situation

b) Is the  function discrete or continuous.

Solution :

1 feet = 12 inches

2 foot = 24 inches

a) Space occupied by 4 inches frames = 4x

Space occupied by 8 inch frames = 8y

4x + 8y = 24

b) The function must be discrete, because values of x must be integer and countable.