Question

You decide to take advantage of the current online dating craze and start your own Web site. You know that you have 600 people who will sign up immediately and, through a careful marketing research and analysis, determine that membership can grow by 25 percent in the first two years, 22 percent in year 3, and 18 percent in Year 4. How many members do you expect to have at the end of four years? (Round intermediate calculations to 6 decimal places, in all cases round your final answer to the nearest whole number.)

Answer 1

1350

Explanation:

Given:

Initial number of members = 600

Now,

Expected members = Initial members × ( 1 + r )ⁿ

by geometric progression

here,

r is the growth rate

n is the number of years

thus,

Number of members that expect at the end of 2 year

Expected members = Initial members × ( 1 + r )ⁿ

r = 25%

n = 2 years

Expected members = 600 × ( 1 + 0.25 )²

= 937.5

similarly,

Numbers of members that expect at the end of 3 year

Expected members = Initial members × ( 1 + r )ⁿ

r = 22%

n = 1 years (i.e after the end of 2 year)

Initial members = 937.5 (i.e after the end of 2 years is the initial for the starting of third year )

Expected members = 937.5 × ( 1 + 0.22 )¹

= 1143.75

Numbers of members that expect at the end of 4 year

Expected members = Initial members × ( 1 + r )ⁿ

r = 18%

n = 1 years (i.e after the end of 3 year)

Initial members = 1143.75 (i.e after the end of 3 years is the initial for the starting of fourth year )

Expected members = 1143.75 × ( 1 + 0.18 )¹

= 1349.625

Hence,

Total expected people = 1349.625 ≈ 1350