The table shows number of people as a function of time in hours. Write an equation for the function and describe a situation that it could represent. Include the initial value, rate of change, and what each quantity represents
in the situation.

Equation ⇒ y = 50x + 100

The initial value = 100

Rate of change = 50

Step-by-step explanation:

The rest of the question is the table:

                    Hours:   1       3     5   ⇒  x

Number of people: 150 250 350  ⇒  y

By graphing the points as (x,y) ⇒ (1,150) , (3,250) and (5,350)

The table will represent a linear function

The general equation of the line ⇒ y = mx + c

where m is the rate of change

And c is the y-intercept or the initial value.

m = (y₂ - y₁)/(x₂ - x₁) = (350 - 250)/( 5 - 3) = 100/2 = 50

∴ y = 50x + c

at x = 1 y = 150

∴ 150 = 50 + c

∴ c = 150 - 50 = 100

∴ y = 50x + 100

See the attached figure.

The situation could represents a general institution introduces services to the people, at the beginning there are 100 people , and each hour the number of people increases 50 persons.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

what is the model?

step-by-step explanation: