Math Question?

Question

Question: A club starts with 10 people and 4 people are added every week after that

a) is this a linear equation?
b)find the linear growth equation to find the club population after 8 weeks
c.) population after 5 months
d.)after how many weeks will the club population be 70

Answer 1

PART A:

Let x = the number of weeks...

y = 10 + 4x

which when written in general line format of y = mx + b ... becomes...

y = 4x + 10

Yes, this is a line. The reason being that you have 10 people.... and each time x increases by 1 (x = week 1, x = week 2, x = week 3,...) you get for more people...

4(1), 4(2), 4(3).... see?

PART B:

Let P represent population... and W represent the number of weeks...

P = 4W + 10, where W = 8

You would be finding P(8) = 4(8) + 10 = 42 people

PART C:

5 months is really dependent on how many weeks are in each month... some have 4 weeks, others have 5.... Assume that each month M has 4 weeks... that means that W = 4M

To determine after so many months what the population is, the P = 4W + 10 equation now becomes P = 4(4M) + 10, substituting 4M for "W".... which simplifies to P = 16M + 10

So... P = 16M + 10, where M = 5 months

You would be finding P(5) = (16)(5) + 10 = 90 people

PART D:

To find how many "weeks" it will takes for there to be a population of 70, we have to go to the population formula that was used when given weeks (W)....

That would be the P = 4W + 10 equation, however, you are going to solve for W, given P = 70.

P = 4W + 10

70 = 4W + 10

add -10 to both sides...

70 - 10 = (4W + 10) - 10

** combine "like" terms **

60 = 4W which is the same as writing 4W = 60

Divide both sides by 4...

4W / 4 = 60 / 4

The 4's on the left cancel out leaving you with...

W = 15

That means that after 15 weeks, the club population P will be 70 people....

Answer 2

a) yup
b) y=10+4x ; where x represents the number of weeks
y is the club population after x weeks
y=42 after 8 weeks
c) y=90 after 5 months
d) x=15 (since 70=10+4x)

Answer 3

a) yes. it is a linear relationship that can be expressed as a linear equation. ( y = mx + b; degree = 1)

b) C = 10+4N (N=#weeks, c= club members)
after 8 weeks its 10+4(8)=10+32=42

c) 5 months=20 weeks so 10+4(20)=90
d) 70=C
70=10+4N
60=4N
60/4 = N
15 = N

Answer 4

a.) yes.
b.) y=4x+10
y is total population of the club
x is week. 4x because four people are added each week
10 is the y-intercept because the club started with 10 people.
y=4(8)+10
y=42 people

c.) 5 months is about 20 weeks.
y=4(20)+10
y=90 people after 20 weeks

d.) now to do this, use translating formulas to get the equation into x=? form
y=4x+10
subtract ten from both sides
y-10=4x
divide by four on each side
x=(y-10)/4
now plug in 70 people where y is.
x=(70-10)/4
x=15.
15 weeks

Answer 5

10 + 4x
x is number of weeks i think thats the equation thingy
after 8 weeks it would be 42 people
5 months = 90 people
population of 70 = 15 weeks

Answer 6

a. yes
b. y=10+4x
y=10+4(8)
y=42
c. y=10+4(4x5)
y=90
d.70=10+4x
60+4x
x=15

Answer 7

a yes
b. ???
c. 30
d. 15weeks