Question

modeling real life the linear function m = 10 - 1.44p represents the amount m (in dollars) of money that you have after printing p photographs.
a. interpret the terms and coefficient in the equation.
b. find the domain of the function.
o 0, 1, 2, 3, 4, 5, 6
o -1.5, -2.5, -3.5, -4.5, -6.5, -7.5, -8.5
o all the real numbers greater than 0
o all whole numbers less than 100
is the domain discrete or continuous?
the domain is
explain.

Explanation:

Step1: Interpret terms and coefficient

The constant term 10 represents the initial amount of money (in dollars) before printing any photographs. The coefficient - 1.44 of p means that for each photograph printed, the amount of money decreases by $1.44.

Step2: Find domain of the function

The number of photographs p cannot be negative (you can't print a negative - number of photographs) and is likely to be a whole number (you can't print a fraction of a photograph in a practical sense). Also, when m = 0, we solve 0=10 - 1.44p for p:
\[1.44p=10\]
\[p=\frac{10}{1.44}\approx6.94\]
Since p is a non - negative whole number and we can't have a fraction of a photograph, p can be 0, 1, 2, 3, 4, 5, 6.

Step3: Determine if domain is discrete or continuous

The domain is discrete because the values of p (number of photographs) are distinct, separate values (whole numbers) and not an unbroken interval of real numbers.

Answer:

a. The constant 10 is the initial money amount. The coefficient - 1.44 means cost per photograph is $1.44.
b. 0, 1, 2, 3, 4, 5, 6; Discrete; Because the number of photographs p is a non - negative whole number and not an unbroken interval of real numbers.