Question

Membership in an art club is expected to grow by about 4% per month. Currently, there are 350 members in the club. In about how many months will membership reach 500 members?

A. 9 months
B. 12 months
C.14 months
D.20 months

Answer 1

500=350(1+0.04/12)^12x
Solve for x
500/350=(1+0.04/12)^12x
X=(Log(500/350)/log(1+0.04/12))/12
X=9 months

Answer 2

A. 9 months

Explanation:

We are given that,

Initial members in the club = 350

Rate of growth of the members = 4% = 0.04

Since, the exponential growth function is given by
`y=a(1+r)^x`, where a= initial value and r= rate of increase and x= time.

Substituting the values, we have,

Number of increase in the members after 'x' months is,

`y=350(1+0.04)^x\\\\y=350(1.04)^x`

Now, the number of months when the number of members is 500 is,

`y=350(1.04)^x\\\\500=350(1.04)^x\\\\1.43=(1.04)^x\\\\\log 1.43=x\log 1.04\\\\x=(\log 1.43)/(\log 1.04)\\\\x=(0.155)/(0.017)\\\\x=9`

That is, after 9 months, the number of members will be 500.

So, option A is correct.