Question

A new urban area has a basketball centre built. It the first year, 2015 the club based at the stadium has 50 members but expects this number to increase by 30 per year. The centre currently has the capacity to hold 400 members, however has been granted permission to extend, when required, to house the rest of the basketball community. If it takes 2 years to plan and build the extension, when should the club start the

process of extending the centre?

(I REALLY NEED HELP WITH THIS QUESTION, IT MAKES NO SENSE TO ME!) ​

Answer 1

Explanation:

they say the club started with 50 members, so

m0= 50

and they expect they'll increase by 30 members per year

you can write this as a lineal function,

with the y-intercept being m0=50

because that's the value for your dependent variable when your independent variable year=0

and your slope is the increase of 30 members per year

so the lineal function is

members = 30year + 50

when will the club reach 400 members?

400 = 30y + 50

11,7=y

they'll reach 400 members when the club reaches its 11,7 years

now since the extension process takes 2 years , they'll need to start 2 years before

11,7 - 2 = 9,7

they'll need to start when the club reaches 9,7 years since its foundation

hope it was helpful!

Answer 2

the club should start the process of extending the center in 2024 or 9 years after 2015

Explanation:

Since it takes 2 years to build the extension, the club should start the process of extending the center 2 years before it reaches its carrying capacity of 400.

Initially, In the year 2015, it has 50 members.

The number of members increase by 30 per year.

This follows a linear equation

y = mx + b,

where y = number of members and x = number of years

initially, x = 0 and y = 50. so,

50 = b

since each year the number of members increases by 30, the slope m is 30,e.g.

for in the 2nd year,(after 1 year has passed)

y = 30(1) + 50

y = 80 members,

now, we have to find the number of years when the stadium reaches maximum capacity and then subtract that by 2 years to find the year when the club should start the extension process,

capacity = 400,

then

400 = 30x + 50

400 - 50 = 30x

350 = 30x

350/30 = x

x = 11.67 years,

This is when the stadium reaches maximum capacity,

We subtract this by 2, to get,

x = 9.67 years,

so, we should start to build the extension 9.67 years after 2015, but to get a whole number, we round down to get,

x = 9 years

or, the club should start the process of extending the center in 2024