Respuesta :
12226 stores will be there in 2016
Solution:
The growth function is given as:
[tex]y = a(1+r)^t[/tex]
Where,
y is the future value
a is the initial value
r is the growth rate
t is the number of years
From given,
In 2000, a company had 1147 stores nationwide
By 2002, this total had grown to 1542
Therefore,
y = 1542
a = 1147
t = 2000 to 2002 = 2 years
r = ?
Substituting we get,
[tex]1542 = 1147(1+r)^2\\\\(1+r)^2 = \frac{1542}{1147}\\\\(1+r)^2 = 1.34437[/tex]
Taking square root of both sides
[tex]1+ r = 1.1594\\\\r = 1.1594 - 1\\\\r = 0.1594[/tex]
If the number of stores continues to grow exponentially at the same rate, how many stores will there be in 2016?
Therefore,
y = ?
a = 1147
r = 0.1594
t = 2000 to 2016 = 16 years
Substituting we get,
[tex]y = 1147(1 + 0.1594)^{16}\\\\y = 1147(1.1594)^{16}\\\\y = 1147 \times 10.6593\\\\y = 12226.3311 \approx 12226[/tex]
Thus 12226 stores will be there in 2016
