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Buying one movie ticket online costs $16.50. Two tickets cost $30.50. Assuming that the relationship is linear, use the drop down menus to complete the recursive formula, the function to represent the cost C of n tickets bought online, and the domain of the function. recursive formula: an=an−1 + ; a1 = function: C(n) = + domain: {0, , . . .}

Respuesta :

calculista

Answer:

[tex]C(n)=14n+2.50[/tex]

Step-by-step explanation:

Let

n -----> number of tickets

C ----> represent the cost of buy n tickets online

we have the ordered pairs

(1,16.50) and (2,30.50)

Find out the slope of the linear equation

The formula to calculate the slope between two points is equal to

[tex]m=\frac{C2-C1}{n2-n1}[/tex]

substitute the values

[tex]m=\frac{30.50-16.50}{2-1}[/tex]

[tex]m=14[/tex]

Find the equation of the line in slope intercept form

[tex]C=m(n)+b[/tex]

we have

[tex]m=14[/tex]

[tex]point(1,16.50)[/tex]

substitute

[tex]16.50=14(1)+b[/tex]

[tex]b=16.50-14[/tex]

[tex]1b=2.50[/tex]

substitute

[tex]C(n)=14n+2.50[/tex]

The domain of the function is all positive integers (whole numbers) including zero

{0,1,2,3,4,...}

MrRoyal

The cost of movie tickets follows an arithmetic pattern.

  • The recursive formula is [tex]\mathbf{C(n)= C(n-1) + 14}[/tex]
  • The domain of the function is: [tex]\mathbf{[0,\infty)}[/tex]

The given parameters are:

[tex]\mathbf{a_1 = 16.50}[/tex] --- the cost of one movie ticket

[tex]\mathbf{a_2 = 30.50}[/tex] --- the cost of two movie tickets

(a) The recursive formula

Express 30.50 as 16.50 + 14

[tex]\mathbf{a_2 = 16.50 + 14}[/tex]

Substitute [tex]\mathbf{a_1 = 16.50}[/tex]

[tex]\mathbf{a_2 = a_1 + 14}[/tex]

Express 1 as 2 -1

[tex]\mathbf{a_2 = a_{2-1} + 14}[/tex]

Substitute n for 2

[tex]\mathbf{a_n = a_{n-1} + 14}[/tex]

Express as a function

[tex]\mathbf{C(n)= C(n-1) + 14}[/tex]

Hence, the recursive formula is [tex]\mathbf{C(n)= C(n-1) + 14}[/tex]

(b) The domain

The number of tickets cannot be negative.

So, the domain of the function is: [tex]\mathbf{[0,\infty)}[/tex]

Read more about functions at:

https://brainly.com/question/1632425

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