Question

A graph has years since group formed on the x-axis, and number of members on the y-axis. A line goes through points (2, 38) and (5, 80).

The membership of a student group is expressed by the equation y = 14x + 10, where x represents the number of years since the group was formed and y represents the number of members.

How many years will it take for the group to have 290 members? A.2 B.12 C.20 D.40
If the group was formed in the year 2000, in what year would you expect the group to have 290 members? A.2000 B.2012 C.2020 D.2029

Please help for both fast

Answer 1

The answer is A. Membership grows by 14 each year.

Step-by-step explanation: Got it right on Edu

Answer 2

20 years will take for the group to have 290 member. In the year 2020 the group have 290 members, if the group was formed in the year 2000.

Explanation:

The given is,

Points ( 2, 38 ) and ( 5, 80 )

Equation,
`y = 14x+10`...............................(1)

Where, x - number of years since the group was formed

y - number of members

Step:1

The given points are verifies the equation for the values relation between members and year of group,

If we apply x=2 years, the answer becomes members y=38. similarly for point (5, 80).

Step:2

For the first question,

Members, y = 290

From equation (1),

290 = 14 (x) + 10

290 - 10 = 14 (x)

280 = 14 (x)

x =
`(280)/(14)`

x = 20

No. of years, x = 20 years

Step:3

For second question,

From the step 1, 20 years will take for the group to have 290 members,

Group formed year = 2000

For 290 members = Group formed year + Years to have 290 members

= 2000+20

= 2020

For 290 members = 2020

Result:

20 years will take for the group to have 290 member. In the year 2020 the group have 290 members, if the group was formed in the year 2000.